Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form.
-$( 4,3 ) ; m = - \frac { 2 } { 3 }$
A) $y = - \frac { 2 } { 3 } x + \frac { 3 } { 17 }$
B) $y = - \frac { 2 } { 3 } x + \frac { 17 } { 3 }$
C) $y = - \frac { 3 } { 2 } x + \frac { 17 } { 3 }$
D) $y = - \frac { 2 } { 3 } x - \frac { 17 } { 3 }$

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. Given the slope $m = -\frac{2}{3}$ and a point $(4,3)$, we can substitute these values into the slope-intercept form to find $b$. Substituting $x = 4$ and $y = 3$ gives $3 = -\frac{2}{3}(4) + b$, solving for $b$ gives $b = \frac{17}{3}$. Therefore, the equation is $y = -\frac{2}{3}x + \frac{17}{3}$.

Write an Equation of the Line Through the Given Point (4,3);m=−23( 4,3 ) ; m = - \frac { 2 } { 3 }(4,3);m=−32​

Write an Equation of the Line Through the Given Point $( 4,3 ) ; m = - \frac { 2 } { 3 }$