Question

1. what is the equation of a line parallel to y - 7 = -\frac{1}{2}(x + 2) that passes through (-4, 1)?

Explanation:

Step1: Identify the slope of the given line

The given line is in point - slope form $y - y_1=m(x - x_1)$. For the line $y - 7=-\frac{1}{2}(x + 2)$, the slope $m =-\frac{1}{2}$. Parallel lines have the same slope.

Step2: Use the point - slope form to find the equation of the new line

The point - slope form is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-4,1)$ and $m =-\frac{1}{2}$. Substitute these values:
$y - 1=-\frac{1}{2}(x+4)$

Step3: Simplify the equation

Expand the right - hand side: $y - 1=-\frac{1}{2}x-2$. Then add 1 to both sides to get the slope - intercept form.
$y=-\frac{1}{2}x - 1$

Answer:

$y=-\frac{1}{2}x - 1$