Question

what is an equation of the line that passes through the point (-3,5) and is parallel to the line x - y = 4?

Explanation:

Step1: Rewrite the given line in slope - intercept form

Rewrite $x - y=4$ as $y=x - 4$. The slope of this line is $m = 1$ since the equation is in the form $y=mx + b$ where $m$ is the slope. Parallel lines have the same slope.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-3,5)$ and $m = 1$. Substitute these values: $y - 5=1\times(x-(-3))$.

Step3: Simplify the equation

$y - 5=x + 3$. Then, rewrite it in slope - intercept form: $y=x+8$.

Answer:

$y=x + 8$