what is the equation of the line that is parallel to the given line and passes through the point (-2…

Explanation:

Step1: Find the slope of the given line

The slope - formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(-5,-4)$ and $(0,-3)$ on the given line, we have $m=\frac{-3-(-4)}{0 - (-5)}=\frac{-3 + 4}{0+5}=\frac{1}{5}$. Parallel lines have the same slope. So the slope of the required line is also $m=\frac{1}{5}$.

Step2: Use the point - slope form to find the equation of the line

The point - slope form is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-2,2)$ and $m = \frac{1}{5}$. Substitute these values: $y - 2=\frac{1}{5}(x+2)$.

Step3: Convert to slope - intercept form

Expand the right - hand side: $y - 2=\frac{1}{5}x+\frac{2}{5}$. Then add 2 to both sides. Since $2=\frac{10}{5}$, we get $y=\frac{1}{5}x+\frac{2}{5}+\frac{10}{5}=\frac{1}{5}x+\frac{12}{5}$.

Answer:

$y=\frac{1}{5}x+\frac{12}{5}$