Solve the problem.
-Given $f ( x ) = m x + b$, find $m$ and $b$ if $f ( - 6 ) = - 7$ and $f ( - 12 ) = - 11$.
A) $m = \frac { 3 } { 2 } ; b = - 3$
B) $m = \frac { 3 } { 2 } ; b = 3$
C) $m = \frac { 2 } { 3 } ; b = 3$
D) $m = \frac { 2 } { 3 } ; b = - 3$

Question

Quizplus · Accepted Answer

To find $m$ and $b$, we can use the given points $(-6, -7)$ and $(-12, -11)$ in the equation $f(x) = mx + b$. Substituting the first point gives us $-7 = m(-6) + b$, and the second point gives us $-11 = m(-12) + b$. Solving these two equations simultaneously for $m$ and $b$ yields $m = \frac{2}{3}$ and $b = -3$.

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