Question

write the equation of the line parallel to the given line and passing through the given point. 2x - 3y = 6, (-1, 4) answer

Explanation:

Step1: Convert to slope-intercept form

Rearrange $2x - 3y = 6$ to solve for $y$:
$-3y = -2x + 6$
$y = \frac{2}{3}x - 2$

Step2: Identify parallel line slope

Parallel lines have equal slopes, so $m = \frac{2}{3}$.

Step3: Use point-slope form

Substitute $m = \frac{2}{3}$ and point $(-1, 4)$ into $y - y_1 = m(x - x_1)$:
$y - 4 = \frac{2}{3}(x - (-1))$

Step4: Simplify to standard form

Expand and rearrange the equation:
$y - 4 = \frac{2}{3}(x + 1)$
$3(y - 4) = 2(x + 1)$
$3y - 12 = 2x + 2$
$2x - 3y = -14$

Answer:

$2x - 3y = -14$