Write an equation in slope-intercept form of the line that passes through the point $\left( - \frac { 3 } { 2 } , \frac { 1 } { 7 } \right)$ and has a slope of $m = - \frac { 2 } { 3 }$ .
A) $y = - \frac { 2 } { 3 } x - \frac { 6 } { 7 }$
B) $y = \frac { 2 } { 3 } x - \frac { 7 } { 6 }$
C) $y = - \frac { 2 } { 3 } x - \frac { 7 } { 6 }$
D) $y = \frac { 2 } { 3 } x - \frac { 6 } { 7 }$
E) $y = - \frac { 2 } { 3 } x + \frac { 6 } { 7 }$

Question

Quizplus · Accepted Answer

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We are given that the slope is $m = - \frac { 2 } { 3 }$ and the line passes through the point $\left( - \frac { 3 } { 2 } , \frac { 1 } { 7 } \right)$. We can substitute these values into the slope-intercept form to get:$$y = - \frac { 2 } { 3 } x + b$$$$ \frac { 1 } { 7 } = - \frac { 2 } { 3 } \left( - \frac { 3 } { 2 } \right) + b$$$$ \frac { 1 } { 7 } = 1 + b$$$$ b = \frac { 6 } { 7 }$$Therefore, the equation of the line in slope-intercept form is $y = - \frac { 2 } { 3 } x + \frac { 6 } { 7 }$.

Write an Equation in Slope-Intercept Form of the Line That (−32,17)\left( - \frac { 3 } { 2 } , \frac { 1 } { 7 } \right)(−23​,71​)

Write an Equation in Slope-Intercept Form of the Line That $\left( - \frac { 3 } { 2 } , \frac { 1 } { 7 } \right)$