# Pre-Algebra : Graphing Lines

## Example Questions

### Example Question #21 : Graphing Lines

What is the slope of the line formed by the following equation?

Explanation:

To find the slope of the line, we must write the equation in slope-intercept form or

where m is the slope and b is the y-intercept.

We must get y by itself. So, we will divide all terms by 4.

Now that it is in slope-intercept form, we can find the slope. The slope m is the coefficient of the term with the variable x. Therefore, the slope of the line

is -2.

### Example Question #22 : Graphing Lines

Find the line that is parallel to the following line:

Explanation:

To find a line that is parallel, we must find a line with the same slope as

When looking at an equation of a line in y-intercept form

we know m is the slope.  So, to determine the slope, we must write the equations in slope-intercept form.  Let's look at the equation

and write it in slope intercept form.  We must divide each term by 9.

Therefore, the slope of this line is -3.  Because it has the same slope as the original equation, this line is parallel to the original line.

### Example Question #23 : Graphing Lines

Find the y-intercept in the following equation:

Explanation:

To find the y-intercept, we must first write the equation in y-intercept form

where b is the y-intercept. So,

we must solve for y.  We must divide each term by 3.  We get

Therefore, the y-intercept is -9.

### Example Question #24 : Graphing Lines

What is the slope of the line that contains the points  and ?

Explanation:

To find the slope of a line with two points we must properly plug the points into the slope equation:

We must then assign the variables  and .

In this case we will plug in for  and  for .

Plugging the points into the equation yields .

Perform the math to arrive at .

### Example Question #25 : Graphing Lines

Find the y-intercept of the following equation of a line:

Explanation:

To find the y-intercept of an equation, we must first write it in slope-intercept form

where m is the slope and b is the y-intercept. So, in our equation of a line, we must solve for y.

We must divide each term by 3.

where -4 is the slope and 12 is the y-intercept.

Therefore, the y-intercept is 12.