Chapter 1.4, Problem 5QR

To determine

To Find: An equation for the specified line.

Answer to Problem 5QR

The equation is $y=\frac{3}{2}x+6$ .

Explanation of Solution

Given information:

The line is passing through $\left(-2,3\right)$ and have a slope $\frac{3}{2}$ .

Concept used:

The equation of a line is given by $y=mx+b$ , where m is the slope of the line, b is the y -intercept.

Calculation:

It is given that the line is passing through $\left(-2,3\right)$ .

Put $\left(x,y\right)=\left(-2,3\right)$ along with $m=\frac{3}{2}$ in $y=mx+b$ .

  $\begin{array}{c}3=\left(\frac{3}{2}\right)\left(-2\right)+b\\ b=3+3\\ b=6\end{array}$

Now put $b=6$ and $m=\frac{3}{2}$ in $y=mx+b$ for the equation of the line.

  $y=\frac{3}{2}x+6$ .

Conclusion:

The equation is $y=\frac{3}{2}x+6$ .