Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Which equation has a slope of $\frac{\mathbf{-}\mathbf{2}}{\mathbf{3}}$and a $\mathit{y}$-intercept of 6?

A$\mathit{y}\mathbf{=}\mathbf{6}\mathit{x}\mathbf{+}\frac{\mathbf{2}}{\mathbf{3}}$

B$\mathit{y}\mathbf{=}\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}}\mathit{x}\mathbf{-}\mathbf{6}$

C$\mathit{y}\mathbf{=}\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}}\mathit{x}\mathbf{+}\mathbf{6}$

D$\mathit{y}\mathbf{=}\mathbf{6}\mathit{x}\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}}$

Short answer

The equation of the line having slope of $-\frac{2}{3}$and a $y$-intercept of 6 is $\mathit{y}\mathbf{=}\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}}\mathit{x}\mathbf{+}\mathbf{6}$.

Therefore, the option Cis correct.

Step-by-step solution

Step 1. Write the form of equation of the line in slope-intercept form.

The equation of the line in slope-intercept form is $y=mx+c$, where$m$ is the slope of the line and$c$ is the $y$-intercept of the line.

Step 2. Determine which equation has a slope of −23 and a y-intercept of 6.

It is given that the slope of the line is $-\frac{2}{3}$. Therefore, the value of $m$is $-\frac{2}{3}$.

It is given that the $y$-intercept of the line is 6. Therefore, the value of $c$is 6.

Substitute $-\frac{2}{3}$and 6 for $m$and $c$respectively in the equation $y=mx+c$.

$\begin{array}{c}y=mx+c\\ y=\frac{-2}{3}x+6\end{array}$

Therefore, the equation of the line having slope of $-\frac{2}{3}$and a $y$-intercept of 6 is $y=\frac{-2}{3}x+6$.

Therefore, the option C is correct.