Question

write the equation of the line that... passes through (-10, -3) and runs parallel to the line y = \frac{2}{5}x - 2. step 1: identify the slope of the given line and its parallel slope. step 2: use point - slope form. y - y_1 = m(x - x_1) step 3: convert to slope - intercept form (optional)

Explanation:

Step1: Identify parallel slope

The slope of the line $y = \frac{2}{5}x - 2$ is $m=\frac{2}{5}$. Parallel lines have equal slopes, so the slope of the new - line is also $m=\frac{2}{5}$.

Step2: Use point - slope form

The point - slope form is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-10,-3)$ and $m = \frac{2}{5}$. Substitute these values:
$y-(-3)=\frac{2}{5}(x - (-10))$
$y + 3=\frac{2}{5}(x + 10)$

Step3: Convert to slope - intercept form

Expand the right - hand side:
$y+3=\frac{2}{5}x+4$
Subtract 3 from both sides:
$y=\frac{2}{5}x+1$

Answer:

$y=\frac{2}{5}x + 1$