Use the given conditions to write an equation for the line in slope-intercept form.
-Slope $= \frac { 2 } { 3 }$, passing through $( 8,5 )$
A) $y = \frac { 2 } { 3 } x - \frac { 1 } { 3 }$
B) $y = \frac { 2 } { 3 } x + \frac { 1 } { 3 }$
C) $y = m x - \frac { 1 } { 3 }$
D) $y = \frac { 2 } { 3 } x + 8$

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 $(8,5)$, we can substitute these values into the slope-intercept equation and solve for $b$: $5 = \frac{2}{3} \cdot 8 + b$, which simplifies to $5 = \frac{16}{3} + b$. Solving for $b$, we get $b = 5 - \frac{16}{3} = \frac{15}{3} - \frac{16}{3} = -\frac{1}{3}$. Therefore, the equation of the line is $y = \frac{2}{3}x - \frac{1}{3}$.

Use the Given Conditions to Write an Equation for the Line