Question

write an equation for line l in point - slope form and slope - intercept form. l is parallel to $y = 4x$.

Explanation:

Step1: Identify slope of parallel line

Parallel lines have equal slopes. For $y=4x$, the slope $m=4$.

Step2: Write point-slope form

Use point $(3,-2)$ and $m=4$. Point-slope formula: $y-y_1=m(x-x_1)$
$y - (-2) = 4(x - 3)$
Simplify sign: $y + 2 = 4(x - 3)$

Step3: Convert to slope-intercept form

Expand the right-hand side:
$y + 2 = 4x - 12$
Subtract 2 from both sides:
$y = 4x - 12 - 2$
$y = 4x - 14$

Answer:

Point-slope form: $y + 2 = 4(x - 3)$
Slope-intercept form: $y = 4x - 14$