Question

What is the equation of the line (in point-slope form) that is parallel to y−8=−(x−2) and passes through the point (−2,4)?

Answer 1

Point-slope form: y - y₁ = m(x - x₁) (x₁ , y₁) is the point, and m is the slope

Since the equation is parallel to y - 8 = -(x - 2), they have the same slope(because they never intersect and go in the same direction), which is -1.

Now that you know the slope (m = -1) and point (-2, 4), you can plug it in:

y - y₁ = m(x - x₁)

y - 4 = -1(x - (-4))

y - 4 = -(x + 4)

Answer 2

y - 4 + -1(x + 2)

Explanation:

Compare your y−8=−(x−2) to

y-k = m(x-h). m is the slope of the line and (h, k) is a point.

We see immediately that the slope of the given line is m = -1.

Starting with point-slope form, y - k = m(x - h), we insert -1 for m and (-2, 4):

y - 4 + -1(x + 2)

This is the desired equation.