question what is an equation of the line that passes through the point (3, -3) and is parallel to the line…

Explanation:

Step1: Find the slope of the given line

Rewrite $5x - 3y=3$ in slope - intercept form $y = mx + b$ (where $m$ is the slope). $-3y=-5x + 3$, so $y=\frac{5}{3}x - 1$. The slope $m=\frac{5}{3}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(3,-3)$ and $m = \frac{5}{3}$. $y-(-3)=\frac{5}{3}(x - 3)$.

Step3: Simplify the equation

$y + 3=\frac{5}{3}x-5$. $y=\frac{5}{3}x-8$.

Answer:

$y=\frac{5}{3}x - 8$