Determine the correct equation for the line passing through the point $( 5 , - 8 )$ and parallel to the line $x + 5 y = 20$.
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

Quizplus · Accepted Answer

Lines that are parallel have the same slope. The given line $x + 5y = 20$ can be rewritten in slope-intercept form as $y = -\frac{1}{5}x + 4$, indicating a slope of $-\frac{1}{5}$. The line passing through $(5, -8)$ with the same slope will have the equation in the form $y = -\frac{1}{5}x + b$. Substituting $x = 5$ and $y = -8$ to find $b$ gives $b = -7$, so the correct equation is $y = -\frac{1}{5}x - 7$.

Determine the Correct Equation for the Line Passing Through the Point