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Linear Equations
 

Linear Equations

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Students learn to define and identify linear equations. They also learn the definition of Standard Form of a linear equation....

Students learn to define and identify linear equations. They also learn the definition of Standard Form of a linear equation.
Students also learn to graph linear equations using x and y intercepts.

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    Linear Equations Linear Equations Presentation Transcript

    • Linear Equations
    • Linear Equations Vocabulary
      • Identify linear equations and functions.
      • Write linear equations in standard form and graph them.
      1) linear equation 2) linear function 3) standard form 4) y-intercept 5) x-intercept
    • Sara has 4 hours after dinner to study and do homework. She has brought home algebra 2 and chemistry. Linear Equations
    • Sara has 4 hours after dinner to study and do homework. She has brought home algebra 2 and chemistry. If she spends x hours on algebra and y hours on chemistry, a portion of the graph of the equation x + y = 4 can be used to relate how much time she spends on each. Linear Equations y x 6 0 4 -2 -2 2 6 -2 6 0 -2 6 2 4
    • Sara has 4 hours after dinner to study and do homework. She has brought home algebra 2 and chemistry. If she spends x hours on algebra and y hours on chemistry, a portion of the graph of the equation x + y = 4 can be used to relate how much time she spends on each. An equation such as x + y = 4 is called a linear equation. Linear Equations y x 6 0 4 -2 -2 2 6 -2 6 0 -2 6 2 4
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. Linear Equations
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. addition Linear Equations
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. addition subtraction Linear Equations
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. addition subtraction multiplication of a variable by a constant Linear Equations
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. addition subtraction multiplication of a variable by a constant The variables may not be multiplied together or appear in a ____________. Linear Equations
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. addition subtraction multiplication of a variable by a constant The variables may not be multiplied together or appear in a ____________. denominator Linear Equations
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. addition subtraction multiplication of a variable by a constant The variables may not be multiplied together or appear in a ____________. A linear equation does not contain variables with exponents other than __. denominator Linear Equations
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. addition subtraction multiplication of a variable by a constant The variables may not be multiplied together or appear in a ____________. A linear equation does not contain variables with exponents other than __. 1 denominator Linear Equations
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. addition subtraction multiplication of a variable by a constant The variables may not be multiplied together or appear in a ____________. A linear equation does not contain variables with exponents other than __. 1 denominator The graph of a linear equation is always a ____. Linear Equations
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. addition subtraction multiplication of a variable by a constant The variables may not be multiplied together or appear in a ____________. A linear equation does not contain variables with exponents other than __. 1 denominator The graph of a linear equation is always a ____. line Linear Equations
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. addition subtraction multiplication of a variable by a constant The variables may not be multiplied together or appear in a ____________. A linear equation does not contain variables with exponents other than __. 1 denominator The graph of a linear equation is always a ____. line Linear Equations Linear Equations
    • A linear equation has no operations other than: ________, ___________, and ____________________________________. addition subtraction multiplication of a variable by a constant The variables may not be multiplied together or appear in a ____________. A linear equation does not contain variables with exponents other than __. 1 denominator The graph of a linear equation is always a ____. line Linear Equations Not Linear Equations Linear Equations
    • A linear function is a function whose ordered pairs satisfy a linear equation. Linear Equations
    • A linear function is a function whose ordered pairs satisfy a linear equation. Any linear function can be written in the form f(x) = mx + b , where m and b are real numbers. Linear Equations
    • A linear function is a function whose ordered pairs satisfy a linear equation. Any linear function can be written in the form f(x) = mx + b , where m and b are real numbers. State whether each function is a linear function. Explain. a) f(x) = 10 – 5x Linear Equations
    • A linear function is a function whose ordered pairs satisfy a linear equation. Any linear function can be written in the form f(x) = mx + b , where m and b are real numbers. State whether each function is a linear function. Explain. a) f(x) = 10 – 5x Yes! Linear Equations
    • A linear function is a function whose ordered pairs satisfy a linear equation. Any linear function can be written in the form f(x) = mx + b , where m and b are real numbers. State whether each function is a linear function. Explain. a) f(x) = 10 – 5x Yes! It can be written as f(x) = – 5x + 10 m = – 5, b = 10 b) g(x) = x 4 – 5 Linear Equations
    • A linear function is a function whose ordered pairs satisfy a linear equation. Any linear function can be written in the form f(x) = mx + b , where m and b are real numbers. State whether each function is a linear function. Explain. a) f(x) = 10 – 5x Yes! It can be written as f(x) = – 5x + 10 m = – 5, b = 10 b) g(x) = x 4 – 5 No! Linear Equations
    • A linear function is a function whose ordered pairs satisfy a linear equation. Any linear function can be written in the form f(x) = mx + b , where m and b are real numbers. State whether each function is a linear function. Explain. a) f(x) = 10 – 5x Yes! It can be written as f(x) = – 5x + 10 m = – 5, b = 10 b) g(x) = x 4 – 5 No! x has an exponent other than 1. Linear Equations
    • A linear function is a function whose ordered pairs satisfy a linear equation. Any linear function can be written in the form f(x) = mx + b , where m and b are real numbers. State whether each function is a linear function. Explain. a) f(x) = 10 – 5x Yes! It can be written as f(x) = – 5x + 10 m = – 5, b = 10 b) g(x) = x 4 – 5 No! x has an exponent other than 1. c) h(x, y) = 2xy Linear Equations
    • A linear function is a function whose ordered pairs satisfy a linear equation. Any linear function can be written in the form f(x) = mx + b , where m and b are real numbers. State whether each function is a linear function. Explain. a) f(x) = 10 – 5x Yes! It can be written as f(x) = – 5x + 10 m = – 5, b = 10 b) g(x) = x 4 – 5 No! x has an exponent other than 1. c) h(x, y) = 2xy No! Linear Equations
    • A linear function is a function whose ordered pairs satisfy a linear equation. Any linear function can be written in the form f(x) = mx + b , where m and b are real numbers. State whether each function is a linear function. Explain. a) f(x) = 10 – 5x Yes! It can be written as f(x) = – 5x + 10 m = – 5, b = 10 b) g(x) = x 4 – 5 No! x has an exponent other than 1. c) h(x, y) = 2xy No! Two variables are multiplied together. Linear Equations
    • To avoid decompression sickness, it is recommended that divers ascend no faster than 30 feet per minute. Linear Equations
    • To avoid decompression sickness, it is recommended that divers ascend no faster than 30 feet per minute. The linear function P(d) = 62.5 d + 217 can be used to find the pressure ( lb/ft 2 ) at a depth of d ft. below the surface of the water. Linear Equations
    • To avoid decompression sickness, it is recommended that divers ascend no faster than 30 feet per minute. The linear function P(d) = 62.5 d + 217 can be used to find the pressure ( lb/ft 2 ) at a depth of d ft. below the surface of the water. Find the pressure at a depth of 350 feet. Linear Equations
    • To avoid decompression sickness, it is recommended that divers ascend no faster than 30 feet per minute. The linear function P(d) = 62.5 d + 217 can be used to find the pressure ( lb/ft 2 ) at a depth of d ft. below the surface of the water. Find the pressure at a depth of 350 feet. P( d ) = 62.5 d + 217 Linear Equations
    • To avoid decompression sickness, it is recommended that divers ascend no faster than 30 feet per minute. The linear function P(d) = 62.5 d + 217 can be used to find the pressure ( lb/ft 2 ) at a depth of d ft. below the surface of the water. Find the pressure at a depth of 350 feet. P( d ) = 62.5 d + 217 P( 350 ) = 62.5( 350 ) + 217 Linear Equations
    • To avoid decompression sickness, it is recommended that divers ascend no faster than 30 feet per minute. The linear function P(d) = 62.5 d + 217 can be used to find the pressure ( lb/ft 2 ) at a depth of d ft. below the surface of the water. Find the pressure at a depth of 350 feet. P( d ) = 62.5 d + 217 P( 350 ) = 62.5( 350 ) + 217 P( 350 ) = 22,092 Linear Equations
    • To avoid decompression sickness, it is recommended that divers ascend no faster than 30 feet per minute. The linear function P(d) = 62.5 d + 217 can be used to find the pressure ( lb/ft 2 ) at a depth of d ft. below the surface of the water. Find the pressure at a depth of 350 feet. P( d ) = 62.5 d + 217 P( 350 ) = 62.5( 350 ) + 217 P( 350 ) = 22,092 Linear Equations The pressure at a depth of 350 feet is about
    • Any linear function can be written in standard form . Linear Equations
    • Any linear function can be written in standard form . Linear Equations Standard Form of a Linear Function
    • Any linear function can be written in standard form . The standard form of a linear function is Ax + By = C , where A > 0, Linear Equations Standard Form of a Linear Function
    • Any linear function can be written in standard form . The standard form of a linear function is Ax + By = C , where A > 0, A and B are not both zero. Linear Equations Standard Form of a Linear Function
    • Any linear function can be written in standard form . The standard form of a linear function is Ax + By = C , where A > 0, A and B are not both zero. Also, A, B, and C are integers whose greatest common factor is 1 Linear Equations Standard Form of a Linear Function
    • The standard form of a linear function is Ax + By = C , where A > 0, A and B are not both zero. Also, A, B, and C are integers whose greatest common factor is 1 Linear Equations Write the equation in Standard Form: Standard Form of a Linear Function
    • The standard form of a linear function is Ax + By = C , where A > 0, A and B are not both zero. Also, A, B, and C are integers whose greatest common factor is 1 Linear Equations Write the equation in Standard Form: Standard Form of a Linear Function
    • The standard form of a linear function is Ax + By = C , where A > 0, A and B are not both zero. Also, A, B, and C are integers whose greatest common factor is 1 Linear Equations Write the equation in Standard Form: Standard Form of a Linear Function
    • The standard form of a linear function is Ax + By = C , where A > 0, A and B are not both zero. Also, A, B, and C are integers whose greatest common factor is 1 Linear Equations Write the equation in Standard Form: Standard Form of a Linear Function
    • In the previous lesson, you graphed functions by using a table of values. Linear Equations
    • In the previous lesson, you graphed functions by using a table of values. Since two points determine a line, there are quicker ways to graph linear functions. Linear Equations
    • In the previous lesson, you graphed functions by using a table of values. Since two points determine a line, there are quicker ways to graph linear functions. One way is to find the points at which the graph intersects each axis and then connect them with a line. Linear Equations y x
    • In the previous lesson, you graphed functions by using a table of values. Since two points determine a line, there are quicker ways to graph linear functions. One way is to find the points at which the graph intersects each axis and then connect them with a line. The y-coordinate of the point at which the graph crosses the y-axis is called the ____________. Linear Equations y x (0, 3)
    • In the previous lesson, you graphed functions by using a table of values. Since two points determine a line, there are quicker ways to graph linear functions. One way is to find the points at which the graph intersects each axis and then connect them with a line. The y-coordinate of the point at which the graph crosses the y-axis is called the ____________. y - intercept Linear Equations y x (0, 3)
    • In the previous lesson, you graphed functions by using a table of values. Since two points determine a line, there are quicker ways to graph linear functions. One way is to find the points at which the graph intersects each axis and then connect them with a line. The y-coordinate of the point at which the graph crosses the y-axis is called the ____________. y - intercept The x-coordinate of the point at which the graph crosses the x-axis is called the ____________. Linear Equations y x (0, 3) (-4, 0)
    • In the previous lesson, you graphed functions by using a table of values. Since two points determine a line, there are quicker ways to graph linear functions. One way is to find the points at which the graph intersects each axis and then connect them with a line. The y-coordinate of the point at which the graph crosses the y-axis is called the ____________. y - intercept The x-coordinate of the point at which the graph crosses the x-axis is called the ____________. x - intercept Linear Equations y x (0, 3) (-4, 0)
    • In the previous lesson, you graphed functions by using a table of values. Since two points determine a line, there are quicker ways to graph linear functions. One way is to find the points at which the graph intersects each axis and then connect them with a line. The y-coordinate of the point at which the graph crosses the y-axis is called the ____________. y - intercept The x-coordinate of the point at which the graph crosses the x-axis is called the ____________. x - intercept Linear Equations y x (0, 3) (-4, 0)
    • Find the x-intercept and the y-intercept of the graph of the equation. Then graph the equation. Linear Equations y x
    • Find the x-intercept and the y-intercept of the graph of the equation. Then graph the equation. The x-intercept is the value of x when y = 0. Linear Equations y x
    • Find the x-intercept and the y-intercept of the graph of the equation. Then graph the equation. The x-intercept is the value of x when y = 0. Linear Equations y x
    • Find the x-intercept and the y-intercept of the graph of the equation. Then graph the equation. The x-intercept is the value of x when y = 0. Linear Equations y x (3, 0)
    • Find the x-intercept and the y-intercept of the graph of the equation. Then graph the equation. The x-intercept is the value of x when y = 0. Linear Equations The y-intercept is the value of y when x = 0. y x (3, 0)
    • Find the x-intercept and the y-intercept of the graph of the equation. Then graph the equation. The x-intercept is the value of x when y = 0. Linear Equations The y-intercept is the value of y when x = 0. y x (0, 5) (3, 0)
    • Find the x-intercept and the y-intercept of the graph of the equation. Then graph the equation. The x-intercept is the value of x when y = 0. Linear Equations The y-intercept is the value of y when x = 0. y x (0, 5) (3, 0)
    • Find the x-intercept and the y-intercept of the graph of the equation. Then graph the equation. The x-intercept is the value of x when y = 0. Linear Equations The y-intercept is the value of y when x = 0. y x (3, 0)
    • Find the x-intercept and the y-intercept of the graph of the equation. Then graph the equation. The x-intercept is the value of x when y = 0. Linear Equations The y-intercept is the value of y when x = 0. y x (3, 0) (0, 5)
    • Find the x-intercept and the y-intercept of the graph of the equation. Then graph the equation. The x-intercept is the value of x when y = 0. Linear Equations The y-intercept is the value of y when x = 0. y x (0, 5) (3, 0)
    • End of Lesson Linear Equations
    • Credits PowerPoint created by Using Glencoe’s Algebra 2 text, © 2005 Robert Fant http://robertfant.com