Determine the correct equation for the line passing through the point (5,-8) and parallel to the line x + 5y = 20.
A) $y = 5 x + 7$
B) $y = - \frac { 1 } { 5 } x - 7$
C) $y = \frac { 1 } { 5 } x + 7$
D) $y = 5 x - 7$
E) $y = - \frac { 1 } { 5 } x - 5$

Question

Determine the correct equation for the line passing through the point (5,-8) and parallel to the line x + 5y = 20. 
A) $y = 5 x + 7$
B) $y = - \frac { 1 } { 5 } x - 7$
C) $y = \frac { 1 } { 5 } x + 7$
D) $y = 5 x - 7$
E) $y = - \frac { 1 } { 5 } x - 5$

Quizplus · Accepted Answer

First, rewrite the given line in slope-intercept form to find its slope: $x + 5y = 20$ becomes $5y = -x + 20$, so $y = -\frac{1}{5}x + 4$. Parallel lines have the same slope, so the slope of the line we're looking for is also $-\frac{1}{5}$. Using the point-slope form of a line, $y - y_1 = m(x - x_1)$, with $m = -\frac{1}{5}$ and the point $(5, -8)$, we get $y + 8 = -\frac{1}{5}(x - 5)$. Simplifying, $y = -\frac{1}{5}x - 8 + 1 = -\frac{1}{5}x - 7$, which matches choice B.

Determine the Correct Equation for the Line Passing Through the Point