Solve the problem.
-Find the equation of the line $y = a x + b$ that passes through the points $( - 4,3 )$ and $( 2 , - 8 )$.
A) $y = - \frac { 11 } { 6 } x - \frac { 13 } { 3 }$
B) $y = - \frac { 5 } { 6 } x - \frac { 6 } { 35 }$
C) $y = - \frac { 13 } { 3 } x - \frac { 11 } { 6 }$
D) $y = - \frac { 11 } { 6 } x + \frac { 19 } { 3 }$

Question

Quizplus · Accepted Answer

To find the equation of the line passing through the points $(-4,3)$ and $(2,-8)$, first calculate the slope $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given points, $m = \frac{-8 - 3}{2 - (-4)} = \frac{-11}{6}$. Then, use one of the points to find $b$ by substituting $m$, $x$, and $y$ into the equation $y = mx + b$. Using $(-4,3)$, $3 = -\frac{11}{6}(-4) + b$, solving for $b$ gives $b = -\frac{13}{3}$. Therefore, the equation is $y = -\frac{11}{6}x - \frac{13}{3}$.

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