Write an equation in slope-intercept form of the line that passes through (1, −9) and (−3, −9).

Answer 1

The slope-intercept form is y = mx + b

From two points we can easily determine the slope, m = (y₂-y₁)/(x₂-x₁)

m = (-9-(-9))/(-3-1) = 0/-4 = 0

Since the slope is 0 we know it's a line parallel to the x-axis.

Using the slope-intercept form, y = 0(x) + b ⇒ y = b

But we don't know what the y-intercept (b) is yet. Using the point-slope form we can determine b

Point-slope: (y - y₁) = m(x - x₁)

(y - (-9)) = 0(x - (-3))

y + 9 = 0

y = -9

So the equation is y = -9.