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2.3 linear equations

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2.3 linear equations

  1. 1. 2.3 Linear EquationsObjectives: I will use the slope-intercept form of a linear equation to graph linear equations. I will use the standard form of a linear equation to graph linear equations.
  2. 2. Identifying a Linear Equation Ax + By = C● The exponent of each variable is 1.● The variables are added or subtracted.● A or B can equal zero.● A>0● Besides x and y, other commonly used variables are m and n, a and b, and r and s.● There are no radicals in the equation.● Every linear equation graphs as a line.
  3. 3. Examples of linear equations2x + 4y =8 Equation is in Ax + By =C form Rewrite with both variables6y = 3 – x on left side … x + 6y =3x=1 B =0 … x + 0 • =1 y-2a + b = 5 Multiply both sides of the equation by -1 … 2a – b = -54x − y = −7 Multiply both sides of the equation by 3 … 4x –y =-21 3
  4. 4. Examples of Nonlinear EquationsThe following equations are NOT in thestandard form of Ax + By =C:4x2 + y = 5 The exponent is 2 x=4 There is a radical in the equationxy + x = 5 Variables are multiplieds/r + r = 3 Variables are divided
  5. 5. x and y -intercepts● The x-intercept is the point where a line crosses the x-axis. The general form of the x-intercept is (x, 0). The y-coordinate will always be zero.● The y-intercept is the point where a line crosses the y-axis. The general form of the y-intercept is (0, y). The x-coordinate will always be zero.
  6. 6. Finding the x-intercept● For the equation 2x + y = 6, we know that y must equal 0. What must x equal?● Plug in 0 for y and simplify. 2x + 0 = 6 2x = 6 x=3● So (3, 0) is the x-intercept of the line.
  7. 7. Finding the y-intercept● For the equation 2x + y = 6, we know that x must equal 0. What must y equal?● Plug in 0 for x and simplify. 2(0) + y = 6 0+y=6 y=6● So (0, 6) is the y-intercept of the line.
  8. 8. To summarize….● To find the x-intercept, plug in 0 for y.● To find the y-intercept, plug in 0 for x.
  9. 9. Find the x and y- intercepts of x = 4y – 5● x-intercept: ● y-intercept:● Plug in y = 0 ● Plug in x = 0 x = 4y - 5 x = 4y - 5 x = 4(0) - 5 0 = 4y - 5 x=0-5 5 = 4y 5 x = -5 =y 4● (-5, 0) is the 5 x-intercept ● (0, 4 )is the y-intercept
  10. 10. Find the x and y-intercepts of g(x) = -3x – 1*● x-intercept ● y-intercept● Plug in y = 0 ● Plug in x = 0 g(x) = -3x - 1 g(x) = -3(0) - 1 0 = -3x - 1 g(x) = 0 - 1 1 = -3x g(x) = -1 1 − ● (0, -1) is the 1 3 =x● ( − 3 , 0) is the y-intercept x-intercept *g(x) is the same as y
  11. 11. Find the x and y-intercepts of 6x - 3y =-18● x-intercept ● y-intercept● Plug in y = 0 ● Plug in x = 0 6x - 3y = -18 6x -3y = -18 6x -3(0) = -18 6(0) -3y = -18 6x - 0 = -18 0 - 3y = -18 6x = -18 -3y = -18 x = -3 y=6● (-3, 0) is the ● (0, 6) is the x-intercept y-intercept
  12. 12. Find the x and y-intercepts of x = 3● x-intercept ● y-intercept● Plug in y = 0. ● A vertical line never crosses the y-axis. There is no y. Why? ● There is no y-intercept.●x = 3 is a vertical line so x alwaysequals 3.● (3, 0) is the x-intercept. x
  13. 13. Find the x and y-intercepts of y = -2● x-intercept ● y-intercept● Plug in y = 0. ● y = -2 is a horizontal line y cannot = 0 because so y always equals -2. y = -2. ● (0,-2) is the y-intercept.● y = -2 is a horizontal x line so it never crosses the x-axis. y●There is no x-intercept.
  14. 14. Graphing Equations● Example: Graph the equation -5x + y = 2 Solve for y first. -5x + y = 2 Add 5x to both sides y = 5x + 2● The equation y = 5x + 2 is in slope-intercept form, y = mx+b. The y-intercept is 2 and the slope is 5. Graph the line on the coordinate plane.
  15. 15. Graphing EquationsGraph y = 5x + 2 x y
  16. 16. Graphing Equations Graph 4x - 3y = 12● Solve for y first 4x - 3y =12 Subtract 4x from both sides -3y = -4x + 12 Divide by -3 -4 12 y = -3 x + -3 Simplify 4 y = 3x – 4 4● The equation y = - 4 is in slope-intercept form, 3x y=mx+b. The y -intercept is -4 and the slope is 4 . 3 Graph the line on the coordinate plane.
  17. 17. Graphing Equations 4Graph y = 3x -4 x y

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