Question

Write an equation in point-slope form and slope-intercept form for each line

1. passes through (1, 9), slope = 2
2. passes through (4, -1), slope = -3

Answer 1

An equation of a line in point-slope form: y - y₁ = m(x - x₁)

1.

passes through (1, 9) ⇒ x₁ = 1, y₁ = 9

slope: m = 2

The equation:

y - 9 = 2(x - 1) ← point-slope form

y - 9 = 2x - 2 {add 9 to both sides}

y = 2x + 7 ← slope-intercept form

2.

passes through (4, -1) ⇒ x₁ = 4, y₁ = -1

slope: m = -3

The equation:

y + 1 = -3(x - 4) ← point-slope form

y + 1 = -3x + 12 {subtract 1 from both sides}

y = -3x + 11 ← slope-intercept form