Solve the problem.
-Find the equation of the line $y = a x + b$ that passes through the points $( - 5,5 )$ and $( 3 , - 9 )$.
A) $y = - \frac { 7 } { 4 } x - \frac { 15 } { 4 }$

B) $y = - \frac { 15 } { 4 } x - \frac { 7 } { 4 }$

C) $y = - \frac { 1 } { 2 } x + 1$

D) $y = - \frac { 7 } { 4 } x + \frac { 15 } { 2 }$

Question

Solve the problem.
-Find the equation of the line $y = a x + b$ that passes through the points $( - 5,5 )$ and $( 3 , - 9 )$.
A) $y = - \frac { 7 } { 4 } x - \frac { 15 } { 4 }$

B) $y = - \frac { 15 } { 4 } x - \frac { 7 } { 4 }$

C) $y = - \frac { 1 } { 2 } x + 1$

D) $y = - \frac { 7 } { 4 } x + \frac { 15 } { 2 }$

Quizplus · Accepted Answer

To find the equation of the line passing through the points $(-5,5)$ and $(3,-9)$, we first calculate the slope $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given points, we get $m = \frac{-9 - 5}{3 - (-5)} = \frac{-14}{8} = -\frac{7}{4}$. Then, using the point-slope form $y - y_1 = m(x - x_1)$ with one of the given points, say $(-5,5)$, we can find $b$. Substituting $m = -\frac{7}{4}$ and the point $(-5,5)$ into the equation, we solve for $b$ and get $b = -\frac{15}{4}$. Thus, the equation of the line is $y = -\frac{7}{4}x - \frac{15}{4}$.

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