Answer:
Parallel: y = 3/7x - 17/7
Perpendicular: y = -7/3x - 11
Step-by-step 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
