Question

write the equation in standard form of the line that is parallel to $y = \frac{5}{4}x - 6$ and passes through the point $(-2, 6)$.$5x - 4y = -24$$-5x = 4y = 6$$5x + 4y = 6$$5x - 4y = -34$

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For $y = \frac{5}{4}x - 6$, the slope $m = \frac{5}{4}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=\frac{5}{4}$, $x_1=-2$, $y_1=6$:
$y - 6 = \frac{5}{4}(x + 2)$

Step3: Convert to standard form

Multiply all terms by 4 to eliminate fraction:
$4y - 24 = 5(x + 2)$
Expand and rearrange to $Ax + By = C$:
$4y - 24 = 5x + 10$
$5x - 4y = -34$

Answer:

$5x - 4y = -34$