what is the equation of the line that is parallel to the given line and passes through the point (-2, 2)?\no…

Explanation:

Step1: Find the slope of the given line

The given line passes through points ((-5,-4)) and ((0, - 3)). 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{-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 of a line 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: (y=\frac{1}{5}x+\frac{2}{5}+2=\frac{1}{5}x+\frac{2 + 10}{5}=\frac{1}{5}x+\frac{12}{5}).

Answer:

(y=\frac{1}{5}x+\frac{12}{5})