Question

What is the equation of the line that has a slope of 13 and goes through the point (6,−2)?

y=13x−8

y=13x

y=13x−4

y=13x+4

Answer 1

y = 13x - 80

{Or, if you mean slope of 1/3: y = ¹/₃x - 4 }

Explanation:

The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:

m = 13

(6, -2) ⇒ x₀ = 6, y₀ = -2

The point-slope form of the equation:

y + 2 = 13(x - 6)

So:

y + 2 = 13x - 78 {subtract 2 from both sides}

y = 13x - 80 ← the slope-intercept form of the equation

{Or, if you mean slope of ¹/₃: m = ¹/₃

The point-slope form of the equation: y + 2 = ¹/₃(x - 6)

y + 2 = ¹/₃x - 2 {subtract 2 from both sides}

y = ¹/₃x - 4 ← the slope-intercept form of the equation}