1. 5.3 Standard Form of a Line

2. 3 3 3 1 33 Finding an Equation Given Two Points Write the equation of the line which contains: (-2, 3) (4, 5) Slope (m)= y 2 - y 1 x 2 - x 1 y = mx + b Slope (m) = 5 - 3 4 - - 2 = 2 6 m = 1 3 y = x + b (x, y) 5 = (4) + b 1 5 = + b 4 b = 5 - 4 3 = 15 3 4 3 - b = 11 3 y = x + 111

3. 4 4 4 Write the equation of the line which contains: (0, - 3) (4, 8) Slope (m)= y 2 - y 1 x 2 - x 1 y = mx + b Slope (m) = 8 - - 3 4 - 0 = 11 4 m = 11 4 y = x + b (x, y) 8 = (4) + b 8 = 11 + b -11 - 11 - 3 = b b = - 3 y = x - 3 11

4. Objective- To graph and manipulate equations in standard form. Standard FormSlope-Intercept Form Ax + By = C y = mx + b 3x + 2y = 8 - 3x 2y = - 3x + 8 2 y = x + -3-3 2 8 2 y = x + 4 -3-3 2 -3-3 2 m = -3-3 2 b = 4 To change Standard Form to Slope-Intercept Form just solve the equation for y.

5. Graph the following equation. - 4x + 3y = 6 +4x 3y = 4x + 6 3 y = x + 4 3 6 3 y = x + 2 4 3 m = 4 3 b = 2 x y +4+4 +3+3

6. Graph the following equation. y = x m = 1 b = 0 x y +1+1 +1+1 y = 1x + 0

7. Convert the following linear equation to standard form. Not in standard form ! Ax + By = C y = 2x + 5 -2x -2x + y = 5 or2x - y = -5

8. - x + y = 4 - x Write a linear equation in standard form given: slope = y-intercept = 4 2 3 y = mx + b y = x + 4 2 3 Not in standard form ! Ax + By = C Where A, B and C are integers. 2 3 2 3 2 3 2 3 No fractional coefficients! 3 - 2x + 3y = 12 or 2x - 3y = - 12

9. - x + y = -1 - x Write a linear equation in standard form given: slope = y-intercept = -1 5 4 y = mx + b y = x - 1 5 4 Not in standard form ! Ax + By = C Where A, B and C are integers. 5 4 5 4 5 4 5 4 No fractional coefficients! 4 - 5x + 4y = -4 or 5x - 4y = 4

10. Objective- To write a linear equation given a point and a slope. Write a linear equation in standard form given: slope = 3 y-intercept = - 2 m = 3 b = - 2 y = 3x + - 2 y = mx + b Not in standard form! Ax + By = C - 3x - 3x + y = - 2 Where A, B and C are integers. or 3x - y = 2

11. - x + y = -2 - x Write a linear equation in standard form given: slope = y-intercept = -2 1 4 y = mx + b y = x - 2 1 4 Not in standard form ! Ax + By = C Where A, B and C are integers. 1 4 1 4 1 4 1 4 No fractions! 4 - x + 4y = -8 or x - 4y = 8

12. 5 x + y = 5 + x 5 5 55 + Write a linear equation in standard form given: slope = point = (2,4) -1 5 y = mx + b y = x + b -1 5 (x,y) 4 = (2) + b -1 5 4 = + b -2-2 5 22 4 = b 2 5 = 22 y = x + -1 5 22 11 5 1 5 5 x + 5y = 22