Question

Consider the line - 3x + 7y=4.

Find the equation of the line that is parallel to this line and passes through the point (-3, -4).
Find the equation of the line that is perpendicular to this line and passes through the point (-3, -4).

Answer 1

Parallel: y = 3/7x - 17/7

Perpendicular: y = -7/3x - 11

Explanation:

Rearrange the given equation so that it is in slope-intercept form.

-3x + 7y = 4

7y = 3x + 4

y = 3/7x + 4/7

The slope of the line is 3/7. A parallel line will have the same slope. Using this slope and the given point, you can find an equation using point-slope form.

y - y₁ = m(x - x₁)

y - (-4) = 3/7(x - (-3))

y + 4 = 3/7(x + 3)

y + 4 = 3/7x + 9/7

y = 3/7x - 17/7

A perpendicular line will have a slope that is the negative inverse of the original slope. This means that the slope will be -7/3. Repeat above steps.

y - y₁ = m(x - x₁)

y - (-4) = -7/3(x - (-3))

y + 4 = -7/3(x + 3)

y + 4 = -7/3x - 7

y = -7/3x - 11