Question

what is an equation of the line that passes through the point (-4,0) and is parallel to the line 5x - 4y = 20?

Explanation:

Step1: Convert to slope-intercept form

Rearrange $5x - 4y = 20$ to $y = mx + b$:
$-4y = -5x + 20$
$y = \frac{5}{4}x - 5$
Parallel lines have equal slopes, so $m = \frac{5}{4}$.

Step2: Use point-slope form

Use point $(-4, 0)$ and $m = \frac{5}{4}$ in $y - y_1 = m(x - x_1)$:
$y - 0 = \frac{5}{4}(x - (-4))$

Step3: Simplify the equation

Simplify the right-hand side and rearrange:
$y = \frac{5}{4}(x + 4)$
$y = \frac{5}{4}x + 5$
Multiply all terms by 4 to eliminate fractions:
$4y = 5x + 20$
$5x - 4y = -20$

Answer:

$5x - 4y = -20$ (or $y = \frac{5}{4}x + 5$)