Chapter 1.4, Problem 4CFU

To determine

To find: the equation of line for the given graph.

Answer to Problem 4CFU

  $y=\frac{1}{2}x-3$

Explanation of Solution

Given information: The graph given is as follows:

  

Calculation From the graph, points on line (x,y) are $\left(0,-3\right)$ and $\left(6,0\right)$ .

At $x=0$ , the y intercept is $-3$ . Thus $b=-3$ .

The point slope formula is as follows:

  $y-y_1=m\left(x-x_1\right)$

Substitute, the given point coordinate and value of b in the point slope formula, to get

  $\begin{array}{c}0-\left(-3\right)=m\left(6-0\right)\\ -3=m\left(6\right)\\ \frac{3}{6}=m\\ \frac{1}{2}=m\end{array}$

The value of m is $\frac{1}{2}$ .

Now, substitute the value of m and b in the slope intercept formula as shown below.

  $\begin{array}{c}y=mx+b\\ y=\frac{1}{2}x+\left(-3\right)\\ y=\frac{1}{2}x-3\end{array}$

Thus, the line equation by point slope method is, $y=\frac{1}{2}x-3$