Question

1. what is the equation of a line parallel to y - 7 = - 1/2(x + 2) that passes through (-4, 1)?
2. what is the equation of a line parallel to y = 1/3x - 4 that passes through (9, 8)?
3. what is the equation of a line parallel to 4x + y = -7 that passes through (2, -9)?

Explanation:

Step1: Recall parallel - line property

Parallel lines have the same slope.

Step2: For question 5

The given line is $y=\frac{1}{3}x - 4$, so the slope $m=\frac{1}{3}$.
Use the point - slope form $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(9,8)$ and $m = \frac{1}{3}$.
$y-8=\frac{1}{3}(x - 9)$
$y-8=\frac{1}{3}x-3$
$y=\frac{1}{3}x + 5$

Step3: For question 6

Rewrite the given line $4x + y=-7$ in slope - intercept form $y=-4x - 7$, so the slope $m=-4$.
Use the point - slope form with $(x_1,y_1)=(2,-9)$ and $m=-4$.
$y+9=-4(x - 2)$
$y+9=-4x + 8$
$y=-4x-1$

Answer:

1. $y=\frac{1}{3}x + 5$
2. $y=-4x-1$