Use the slope-intercept form to write an equation of the line that passes through the given points. Use
function notation where y = f(x).
-$( 2 , - 3 )$ and $( - 7 , - 11 )$
A) $f ( x ) = \frac { 9 } { 8 } x - \frac { 43 } { 9 }$
B) $f ( x ) = \frac { 8 } { 9 } x - \frac { 43 } { 9 }$
C) $f ( x ) = - \frac { 9 } { 8 } x - \frac { 1 } { 9 }$
D) $f ( x ) = - \frac { 8 } { 9 } x - \frac { 1 } { 9 }$

Question

Quizplus · Accepted Answer

First, calculate the slope (m) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ with the given points $(2, -3)$ and $(-7, -11)$, which gives $m = \frac{-11 - (-3)}{-7 - 2} = \frac{-8}{-9} = \frac{8}{9}$. Then, use one of the points and the slope to find the y-intercept (b) using $y = mx + b$. Substituting $x = 2$, $y = -3$, and $m = \frac{8}{9}$ gives $-3 = \frac{8}{9}(2) + b$, solving for b gives $b = -\frac{43}{9}$. Therefore, the equation is $f(x) = \frac{8}{9}x - \frac{43}{9}$.

Use the Slope-Intercept Form to Write an Equation of the Line