The document provides examples of writing linear equations in standard form (Ax + By = C) and point-slope form (y - y1 = m(x - x1)) by converting between the two forms. It also gives examples of finding the slope and y-intercept of a line from two points to write the equation in point-slope and slope-intercept forms. Finally, it demonstrates finding the x- and y-intercepts of lines from their equations and using them to graph the lines.

1. 5.5 Standard and Point-Slope Forms B 5.5 Practice

2. Write each equation in Standard Form. Standard Form : Ax + By = C 1. 7x + 2y - 11 = 0 +11 +11 7x + 2y = 11

3. Write each equation in Standard Form. Standard Form : Ax + By = C 2. 4x = 8y + 10 -8y -8y 4x - 8y = 10

4. Write each equation in Standard Form. Standard Form : Ax + By = C 3. -12x + 2 = 17y - 3 -17y -17y -12x - 17y + 2 = -3 -2 -2 -12x - 17y = -5

5. Write each equation in Standard Form. Standard Form : Ax + By = C 4. 4y = 2x - 8 -2x - 2x -2x + 4y = -8

6. Write an equation in point-slope form for the line that has the given slope and the given point. 5. Slope 3/4, (4, 6) y - ____ = ____(x - ___ ) y - y 1 = m(x - x 1 ) y - _6__ = _ 3/4 _(x - _4_ )

7. Write an equation in point-slope form for the line that has the given slope and the given point. 6. Slope -2, (3, 4) y - ____ = ____(x - ___ ) y - y 1 = m(x - x 1 ) y - _4__ = _ -2 _(x - _3_ )

8. Write an equation in point-slope form for the line that has the given slope and the given point. 7. Slope: -3, (-4, 8) y - ____ = ____(x - ___ ) y - y 1 = m(x - x 1 ) y - _8__ = _ -3 _(x - _-4_ ) y - _8_ = _-3_ (x + 4_)

9. Write an equation in point-slope form for the line that has the given slope and the given point. 8. Slope 1/5, (7, -3) y - ____ = ____(x - ___ ) y - y 1 = m(x - x 1 ) y - _-3__ = _ 1/5 _(x - _7_ ) y + 3_ = _1/5_ (x - 7_)

10. Use each pair of points to write the equation of a line in point-slope form and slope-intercept form. 9. (-3, 3), (-4, 4) Step 1: Identify Slope & Pts slope = rise = y 2 – y 1 = run x 2 – x 1 4 - 3 = -4 - (-3) x 1 , y 1 x 2 , y 2 1 = -1 -1

11. 9. (-3, 3); m = -1 y - ____ = ____(x - ___ ) y - y 1 = m(x - x 1 ) y - _3__ = _ -1 _(x - _-3_ ) Y - 3 = -1 (x + 3 ) Use each pair of points to write the equation of a line in point-slope form and slope-intercept form.

12. 9. Y-intercept (x=0) Y - 3 = -1 (x + 3 ) Use each pair of points to write the equation of a line in point-slope form and slope-intercept form. Y - 3 = -1 (0 + 3 ) Y - 3 = -1 (3) Y - 3 = -3 Y + 3 = +3 Y = 0

13. 9. Slope-intercept Form Y = mx + b Use each pair of points to write the equation of a line in point-slope form and slope-intercept form. M = -1 B = 0 Y = -1x + 0 Y = -x

14. Use each pair of points to write the equation of a line in point-slope form and slope-intercept form. 10. (5, 2), (-2, 5) Step 1: Identify Slope & Pts slope = rise = y 2 – y 1 = run x 2 – x 1 5 - 2 = -2 - 5 x 1 , y 1 x 2 , y 2 3 -7

15. 9. (5, 2); m = -3/7 y - ____ = ____(x - ___ ) y - y 1 = m(x - x 1 ) y - _2__ = _- 3/7 _(x - _5_ ) Use each pair of points to write the equation of a line in point-slope form and slope-intercept form.

16. 10. Y-intercept (x=0) Use each pair of points to write the equation of a line in point-slope form and slope-intercept form. Y - 2 = -3/7 (0 - 5 ) Y - 2 = -3/7 (-5) Y - 2 = 15/7 Y + 2 = + 2 Y = 29/7 = 4 and 1/7 y - _2__ = _- 3/7 _(x - _5_ )

17. 10. Slope-intercept Form Y = mx + b Use each pair of points to write the equation of a line in point-slope form and slope-intercept form. M = -3/7 B = 29/7 Y = -3/7x + 29/7

18. Find the x and y intercepts, and use them to graph the equation. 11. 2x - y = -4 X -intercept - 0 for y 2x - 0 = -4 2x = -4 (-2, 0) 0 - y = -4 2(0) - y = -4 Y-intercept - 0 for x -y = -4 (0, 4) X = -2 y = 4

19. Find the x and y intercepts, and use them to graph the equation. (-2, 0) and (0, 4) x y

20. Find the x and y intercepts, and use them to graph the equation. 12. X - 2y = 2 X -intercept - 0 for y X - 2(0) = 2 X - 0 = 2 (2, 0) - 2y = 2 0 - 2y = 2 Y-intercept - 0 for x Y = -1 (0, -1) X = 2

21. Find the x and y intercepts, and use them to graph the equation. (2, 0) and (0, -1) x y 12.