Chapter 4, Problem 2PT

To determine

To find the given equation in slope-intercept form.

Answer to Problem 2PT

  $y=\frac{2}{3}x-7$

Explanation of Solution

Given:

Line passing through the point $\left(3,-5\right)$ with slope $\frac{2}{3}$ .

Concept used:

Equation of a line passing through the point $\left(x_1,y_1\right)$ with slope m is $y-y_1=m\left(x-x_1\right)$ .

Calculation:

Given,

  $\left(x_1,y_1\right)=\left(3,-5\right)\&m=\frac{2}{3}$

Now the equation of the line is,

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \Rightarrow y-\left(-5\right)=\frac{2}{3}\left(x-3\right)\\ \Rightarrow y+5=\frac{2}{3}x-2\\ \Rightarrow y=\frac{2}{3}x-2-5\\ \Rightarrow y=\frac{2}{3}x-7\end{array}$