Determine the equation of the line described. Put answer in the slope-intercept form, if possible.
-Through $( - 3 , - 14 )$, parallel to $3 x + 8 y = - 65$
A) $y = - \frac { 3 } { 8 } x - \frac { 121 } { 8 }$
B) $y = \frac { 3 } { 8 } x + \frac { 121 } { 8 }$
C) $y = \frac { 3 } { 8 } x - \frac { 65 } { 8 }$
D) $y = - \frac { 8 } { 3 } x - \frac { 14 } { 3 }$

Question

Quizplus · Accepted Answer

Lines that are parallel have the same slope. The given equation $3x + 8y = -65$ can be rewritten in slope-intercept form as $y = -\frac{3}{8}x - \frac{65}{8}$, indicating a slope of $-\frac{3}{8}$. To find the equation of a line parallel to this and passing through $(-3, -14)$, we use the slope $-\frac{3}{8}$ and the point $(-3, -14)$ in the point-slope form $y - y_1 = m(x - x_1)$, which simplifies to $y = -\frac{3}{8}x - \frac{121}{8}$ in slope-intercept form.

Determine the Equation of the Line Described (−3,−14)( - 3 , - 14 )(−3,−14)

Determine the Equation of the Line Described $( - 3 , - 14 )$