Question

write the equation of a line that passes through the point (-6,9) and is parallel to the line shown below.

Explanation:

Step1: Find the slope of the given line

Pick two points on the given line, say $(0, - 2)$ and $(2,0)$. The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{0+2}{2 - 0}=1$.

Step2: Use the point - slope form for the new line

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-6,9)$ and $m = 1$ (since parallel lines have the same slope). Substitute the values: $y-9=1\times(x + 6)$.

Step3: Simplify the equation

Expand the right - hand side: $y-9=x + 6$. Then, rewrite it in slope - intercept form $y=x+15$.

Answer:

$y=x + 15$