Transcript of "Writing and Graphing slope intercept form"
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Objective The student will be able to: <ul><li>Graph linear equations in slope- intercept form. </li></ul><ul><li>write equations using slope-intercept form. </li></ul><ul><li>identify slope and y-intercept from an equation. </li></ul>
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FORMULA FOR FINDING SLOPE The formula is used when you know two points of a line. EXAMPLE
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Find the slope of the line between the two points (-4, 8) and (10, -4) If it helps label the points. Then use the formula
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Graphing Linear Equations In Slope-Intercept Form
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We have already seen that linear equations have two variables and when we plot all the (x,y) pairs that make the equation true we get a line . In this section, instead of making a table, evaluating y for each x, plotting the points and making a line, we will use The Slope-Intercept Form of the equation to graph the line.
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These equations are all in Slope-Intercept Form: Notice that these equations are all solved for y.
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Just by looking at an equation in this form, we can draw the line (no tables). <ul><li>The constant is the y-intercept. </li></ul><ul><li>The coefficient is the slope . </li></ul>Constant = 1, y-intercept = 1. Coefficient = 2, slope = 2. Constant = -4, y-intercept = -4. Coefficient = -1, slope = -1. Constant = -2, y-intercept = -2. Coefficient = 3/2, slope = 3/2.
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The formula for Slope-Intercept Form is: <ul><li>‘ b’ is the y-intercept . </li></ul><ul><li>‘ m’ is the slope . </li></ul>On the next three slides we will graph the three equations: using their y-intercepts and slopes.
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1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1. up 2 right 1 up 2 right 1
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1) Plot the y-intercept as a point on the y-axis. The constant, b = -4, so the y-intercept = -4. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -1, so the slope = -1/1. right 1 down 1 right 1 down 1
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1) Plot the y-intercept as a point on the y-axis. The constant, b = -2, so the y-intercept = -2. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 3/2, so the slope = 3/2. right 2 up 3 right 2 up 3
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<ul><li>Sometimes we must solve the equation for y before we can graph it. </li></ul>The constant, b = 3 is the y-intercept. The coefficient, m = -2 is the slope.
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1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y-intercept = 3. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1. right 1 down 2 right 1 down 2
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Important!!! This is one of the big concepts in Algebra 1. You need to thoroughly understand this! Slope – Intercept Form y = mx + b m represents the slope b represents the y-intercept
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Writing Equations When asked to write an equation, you need to know two things – slope (m) and y-intercept (b). There are three types of problems you will face.
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Writing Equations – Type #1 Write an equation in slope-intercept form of the line that has a slope of 2 and a y-intercept of 6. To write an equation, you need two things: slope (m) = y – intercept (b) = We have both!! Plug them into slope-intercept form y = mx + b y = 2x + 6 2 6
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Write the equation of a line that has a y-intercept of -3 and a slope of -4. <ul><li>y = -3x – 4 </li></ul><ul><li>y = -4x – 3 </li></ul><ul><li>y = -3x + 4 </li></ul><ul><li>y = -4x + 3 </li></ul>
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Writing Equations – Type #2 Write an equation of the line that has a slope of 3 and goes through the point (2,1). To write an equation, you need two things: slope (m) = y – intercept (b) = We have to find the y-intercept!! Plug in the slope and ordered pair into y = mx + b 1 = 3(2) + b 3 ???
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Writing Equations – Type #2 1 = 3(2) + b Solve the equation for b 1 = 6 + b -6 -6 -5 = b To write an equation, you need two things: slope (m) = y – intercept (b) = y = 3x - 5 3 -5
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Writing Equations – Type #3 <ul><li>Write an equation of the line that goes through the points (-2, 1) and (4, 2). </li></ul><ul><li>To write an equation, you need two things: </li></ul><ul><li>slope (m) = </li></ul><ul><li>y – intercept (b) = </li></ul><ul><li>We need both!! First, we have to find the slope. Plug the points into the slope formula. </li></ul><ul><li>Simplify </li></ul>??? ???
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Writing Equations – Type #3 <ul><li>Write an equation of the line that goes through the points (-2, 1) and (4, 2). </li></ul><ul><li>To write an equation, you need two things: </li></ul><ul><li>slope (m) = </li></ul><ul><li>y – intercept (b) = </li></ul><ul><li>It’s now a Type #2 problem. Pick one of the ordered pairs to plug into the equation. Which one looks easiest to use? </li></ul><ul><li>I’m using (4, 2) because both numbers are positive. </li></ul><ul><li>2 = (4) + b </li></ul>???
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Writing Equations – Type #3 2 = (4) + b Solve the equation for b 2 = + b To write an equation, you need two things: slope (m) = y – intercept (b) =
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Write an equation of the line that goes through the points (0, 1) and (1, 4). <ul><li>y = 3x + 4 </li></ul><ul><li>y = 3x + 1 </li></ul><ul><li>y = -3x + 4 </li></ul><ul><li>y = -3x + 1 </li></ul>
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To find the slope and y-intercept of an equation, write the equation in slope-intercept form: y = mx + b. <ul><li>Find the slope and y-intercept. </li></ul><ul><li>y = 3x – 7 </li></ul><ul><li>y = m x + b </li></ul><ul><li>m = 3, b = -7 </li></ul>
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Find the slope and y-intercept. <ul><li>2) y = x </li></ul><ul><li>y = m x + b </li></ul><ul><li>y = x + 0 </li></ul><ul><li>3) y = 5 </li></ul><ul><li>y = m x + b </li></ul><ul><li>y = 0x + 5 </li></ul>m = b = 0 m = 0 b = 5
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Find the slope and y-intercept. 4) 5x - 3y = 6 <ul><li>Write it in slope-intercept form. (y = mx + b) </li></ul><ul><li>5x – 3y = 6 </li></ul><ul><li>-3y = -5x + 6 </li></ul><ul><li>y = x - 2 </li></ul>-3 -3 -3 m = b = -2
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<ul><li>Write it in slope-intercept form. (y = mx + b) </li></ul><ul><li>2y + 2 = 4x </li></ul><ul><li> 2y = 4x - 2 </li></ul><ul><li>y = 2x - 1 </li></ul>Find the slope and y-intercept. 5) 2y + 2 = 4x 2 2 2 m = 2 b = -1
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Find the slope and y-intercept of y = -2x + 4 <ul><li>m = 2; b = 4 </li></ul><ul><li>m = 4; b = 2 </li></ul><ul><li>m = -2; b = 4 </li></ul><ul><li>m = 4; b = -2 </li></ul>
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