Chapter 1, Problem 37RE

To determine

To find:The slope and y-intercept and graph the line

Answer to Problem 37RE

The slope of the line is $\frac{4}{5}$ and the y-intercept is 4.

  

Explanation of Solution

Given: $4x-5y=-20$

Formula Used:

Slope-intercept form is $y=mx+b$

Calculation:

Rewrite the equation $4x-5y=-20$ in the form $y=mx+b$ .

Subtract 4x from both sides of the equation.

  $\begin{array}{l}4x-5y-4x=-20-4x\\ -5y=-4x-20\end{array}$

Divide by -5 on both sides of the equation.

  $\begin{array}{l}\frac{-5y}{-5}=\frac{-4x}{-5}-\frac{20}{-5}\\ y=\frac{4}{5}x+4\end{array}$

Compare the equation $y=\frac{4}{5}x+4$ with $y=mx+b$ .

  $y=\frac{4}{5}x+4$

  $y=mx+b$

Therefore, the slope of the line is $\frac{4}{5}$ and the y-intercept is 4.

Since the y-intercept is 4, a point on the line is $\left(0,4\right)$ .

For getting another on the line, start at the point $\left(0,4\right)$ , go 5 units to the right and then up 4 units. We get to the point $\left(5,8\right)$ .

The line $y=\frac{4}{5}x+4$ can be graphed by plotting the points and drawing a line passing through them.

  

Conclusion:

Therefore, the slope of the line is $\frac{4}{5}$ and the y-intercept is 4.