Chapter 8, Problem 15CT

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 15CT

The slope of the lineis $6$ and the y-intercept is $-2$ .

Explanation of Solution

Given:

An equation:

  $-6x+y=-2$ .

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:

  $\begin{array}{l}-6x+y=-2\left(\text{Given equation}\right)\\ -6x+6x+y=-2+6x\left(\text{Adding 6}x\text{ on both sides}\right)\\ y=6x-2\end{array}$

Upon looking at our equation, we can see that the value of m is $6$ and the value of b is $-2$ . Therefore, the slope of the line is $6$ 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 $6$ , so rise is $6$ and run is $1$ .

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