Question

what is an equation of the line that passes through the point (2, -3) and is parallel to the line 5x - 2y = 2?

Explanation:

Step1: Find slope of given line

Rewrite $5x - 2y = 2$ to slope-intercept form $y=mx+b$:
$-2y = -5x + 2$
$y = \frac{5}{2}x - 1$
Slope $m = \frac{5}{2}$

Step2: Use point-slope form

Parallel lines have equal slopes. Use point $(2,-3)$:
$y - (-3) = \frac{5}{2}(x - 2)$

Step3: Simplify to standard form

$y + 3 = \frac{5}{2}x - 5$
Multiply all terms by 2:
$2y + 6 = 5x - 10$
Rearrange terms:
$5x - 2y = 16$

Answer:

$5x - 2y = 16$ (or $y = \frac{5}{2}x - 8$ in slope-intercept form)