Answer:
15. y = 3x + 23
16. y = -2x + 11
17. y = (1/4)x + 6
18. y = x
19. y = (-8/5)x - 4
20. y = (-7/5)x - 5
Explanation:
Point-slope form: y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line
15. y - 2 = 3(x + 7)
⇒ y = 3x + 23
16. y - 5 = -2(x - 3)
⇒ y = -2x + 11
17. y - 7 = (1/4)(x - 4)
⇒ y = (1/4)x + 6
Slope formula: m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line
Point-slope form: y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line
18. let (x1, y1) = (-2, -2)
let (x2, y2) = (-5, -5)
⇒ m = (-5 + 2) / (-5 + 2) = 1
⇒ y + 2 = 1(x + 2)
⇒ y = x
19. let (x1, y1) = (0, -4)
let (x2, y2) = (-5, 4)
⇒ m = (4 + 4) / (-5 - 0) = -8/5
⇒ y + 4 = (-8/5)(x - 0)
⇒ y = (-8/5)x - 4
20. let (x1, y1) = (-5, 2)
let (x2, y2) = (0, -5)
⇒ m = (-5 - 2) / (0 + 5) = -7/5
⇒ y - 2 = (-7/5)(x + 5)
⇒ y = (-7/5)x - 5