Chapter 8.5, Problem 19E

To determine

To identify:

The slope and y -intercept of the line with the given equation. Use the slope and y -intercept to graph the equation.

Answer to Problem 19E

The slope of the lineis $\frac{5}{2}$ and the y -intercept is $2$ .

Explanation of Solution

Given:

An equation: $5x-2y=-4$ .

Concept used:

The slope-intercept form of equation is $y=mx+b$ , where m represents slope of line and b represents the y -intercept.

Calculation:

First of all, we will convert our given equation in slope-intercept form as shown below:

  $\begin{array}{l}5x-2y=-4\left(\text{Given equation}\right)\\ 5x-5x-2y=-4-5x\left(\text{Subtracting }5x\text{from both sides}\right)\\ -2y=-5x-4\\ \frac{-2y}{-2}=\frac{-5x}{-2}-\frac{4}{-2}\left(\text{Dividing both sides by }-2\right)\\ y=\frac{5}{2}x+2\end{array}$

Upon looking at our equation, we can see that the value of m is $\frac{5}{2}$ and the value of b is $2$ . Therefore, the slope of the line is $\frac{5}{2}$ and the y -intercept is $2$ .

We will start from drawing the y- intercept of our given line. The y -intercept of our given line is $2$ , so we will start our line from $(0,2)$ .

Since slope of our given line is $\frac{5}{2}$ , so rise is 5 and run is2.

Upon graphing our given equation, we will get our required graph as shown below: