what is the equation of the line that is parallel to the given line and passes through the point (-3…

Explanation:

Step1: Find the slope of the given line

The slope $m$ of a line passing through two points $(x_1,y_1)=(0,3)$ and $(x_2,y_2)=(3, - 1)$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{-1 - 3}{3-0}=\frac{-4}{3}$. 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 $(x_1,y_1)=(-3,2)$ and $m =-\frac{4}{3}$. Substitute these values: $y - 2=-\frac{4}{3}(x + 3)$.

Step3: Convert to standard form

Expand the right - hand side: $y-2=-\frac{4}{3}x-4$. Multiply through by 3 to clear the fraction: $3y-6=-4x - 12$. Rearrange to get $4x + 3y=-6$.

Answer:

$4x + 3y=-6$