Question

write the equation of the line that is parallel to the graphed line below and passes through (2,0)

Explanation:

Step1: Find the slope of the given line

Pick two points on the given line, say $(-2, 4)$ and $(0, - 2)$. Use the slope - formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m=\frac{-2 - 4}{0+2}=\frac{-6}{2}=-3$. Parallel lines have equal slopes, so the slope of the new line is also $m=-3$.

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 $(x_1,y_1)=(2,0)$ and $m=-3$. Substitute these values: $y-0=-3(x - 2)$.

Step3: Simplify the equation

$y=-3x + 6$.

Answer:

$y=-3x + 6$