Chapter 5.6, Problem 11PPE

To determine

To write an equation in slope-intercept form of the line that passes through the point $\left(0,0\right)$ and parallel to the equation $y=\frac{2}{3}x+1$ .

Answer to Problem 11PPE

The required equation of the line in slope-intercept form is $y=\frac{2}{3}x$ .

Explanation of Solution

Given information :

Givenpoint $\left(0,0\right)$ and equation of the line $y=\frac{2}{3}x+1$ .

Slope of the given line $y=\frac{2}{3}x+1$ is $m=\frac{2}{3}.$

Since the parallel lines are same slope.

Thus, the required equation of the line is $y-y_1=m\left(x-x_1\right)$

Substitute $\left(x_1,y_1\right)=\left(0,0\right)$ and $m=\frac{2}{3}$ in above equation, to get

  $\begin{array}{l}\Rightarrow y-0=\frac{2}{3}\left(x-0\right)\\ \Rightarrow y-0=\frac{2}{3}x\\ \therefore y=\frac{2}{3}x\end{array}$

Hence, the required equation of the line in slope-intercept form is $y=\frac{2}{3}x$ .