Write an equation in slope-intercept form for a line that passes through (5,-8) and is parallel to $5 x + 6 y = 21$ .
A) $y = \frac { 6 } { 5 } x - \frac { 23 } { 6 }$
B) $y = - \frac { 5 } { 6 } x - \frac { 23 } { 6 }$
C) $y = \frac { 5 } { 6 } x + \frac { 23 } { 6 }$
D) $y = - \frac { 5 } { 6 } x - \frac { 43 } { 6 }$
E) $y = - \frac { 6 } { 5 } x - \frac { 23 } { 6 }$

Question

Quizplus · Accepted Answer

First, convert the given equation $5x + 6y = 21$ to slope-intercept form to find the slope of the parallel line. The slope-intercept form is $y = mx + b$, where $m$ is the slope. The given equation becomes $6y = -5x + 21$, so $y = -\frac{5}{6}x + \frac{21}{6}$. Parallel lines have the same slope, so the slope of the line we're looking for is $-\frac{5}{6}$. To find the y-intercept ($b$), use the point (5, -8) and the slope $-\frac{5}{6}$ in the equation $y = mx + b$, which gives $-8 = -\frac{5}{6}(5) + b$. Solving for $b$ gives $b = -\frac{23}{6}$. Therefore, the equation of the line is $y = -\frac{5}{6}x - \frac{23}{6}$.

Write an Equation in Slope-Intercept Form for a Line That 5x+6y=215 x + 6 y = 215x+6y=21

Write an Equation in Slope-Intercept Form for a Line That $5 x + 6 y = 21$