Chapter 1, Problem 43SGA

To determine

To find: the slope-intercept form of line equation.

Answer to Problem 43SGA

  $y=4x-4$

Explanation of Solution

Given information:

  $\begin{array}{l}x-\text{intercept}=1\\ y-\text{intercept}=-4\end{array}$

Calculation:

The coordinates $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ will be $\left(0,-4\right)$ and $\left(1,0\right)$ respectively.

Substitute the values into the slope formula to evaluate slope as follows:

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{0-\left(-4\right)}{1-0}\\ =\frac{4}{1}\\ =4\end{array}$

The slope intercept form of equation is as follows:

  $y=mx+b$

Substitute the values of slope (m) and one of the coordinates $\left(1,0\right)$ in the above equation and solve as follows:

  $\begin{array}{c}y=mx+b\\ 0=\left(4\right)\left(1\right)+b\\ 0=4+b\\ b=-4\end{array}$

Now put the value of m and b in the slope intercept form as shown below.

  $\begin{array}{l}y=mx+b\\ y=4x+\left(-4\right)\\ y=4x-4\end{array}$

Thus, the slope intercept form of line is $y=4x-4$ .