# Intermediate Geometry : How to find the equation of a line

## Example Questions

### Example Question #11 : How To Find The Equation Of A Line

Find the equation for the line passing through the points and .

Explanation:

First, determine the slope of the line using the slope formula:

The equation will be in the form where m is the slope that we just determined, and b is the y-intercept. To determine that, we can plug in the slope for m and the coordinates of one of the original points for x and y:

to subtract, it will be easier to convert 3 to a fraction,

The equation is

### Example Question #12 : How To Find The Equation Of A Line

Write the equation for the line passing through the points and .

Explanation:

First, find the slope of the line:

Now we want to find the y-intercept. We can figure this out by plugging in the slope for "m" and one of the points in for x and y in the formula :

The equation is

### Example Question #13 : How To Find The Equation Of A Line

Find the equation of a line passing through the points  and .

None of these.

Explanation:

To find the equation of a line passing through these points we must find a line with that same slope. Start by finding the slope between the two points and then use the point slope equation to find the equation of the line.

slope:

Now use the point slope equation:

*make sure you use the SAME coordinate pair when substituting x and y into the point slope equation.

### Example Question #14 : How To Find The Equation Of A Line

Find the equation of a line that goes through the points  and .

Explanation:

Recall that the slope-intercept form of a line:

,

where  and .

First, find the slope of the line by using the following formula:

Next, find the y-intercept of the line by plugging in  of the points into the semi-completed formula.

Plugging in  yields the following:

Solve for .

The equation of the line is then .

### Example Question #15 : How To Find The Equation Of A Line

Find the equation of a line that goes through the points  and .

Explanation:

Recall that the slope-intercept form of a line:

,

where  and .

First, find the slope of the line by using the following formula:

Next, find the y-intercept of the line by plugging in  of the points into the semi-completed formula.

Plugging in  yields the following:

Solve for .

The equation of the line is then .

### Example Question #16 : How To Find The Equation Of A Line

Find the equation of a line that goes through the points  and .

Explanation:

Recall that the slope-intercept form of a line:

,

where  and .

First, find the slope of the line by using the following formula:

Next, find the y-intercept of the line by plugging in  of the points into the semi-completed formula.

Plugging in  yields the following:

Solve for .

The equation of the line is then .

### Example Question #17 : How To Find The Equation Of A Line

Find the equation of a line that goes through the points  and .

Explanation:

Recall that the slope-intercept form of a line:

,

where  and .

First, find the slope of the line by using the following formula:

Next, find the y-intercept of the line by plugging in  of the points into the semi-completed formula.

Plugging in  yields the following:

Solve for .

The equation of the line is then .

### Example Question #18 : How To Find The Equation Of A Line

Find the equation of the line that goes through the points  and .

Explanation:

Recall that the slope-intercept form of a line:

,

where  and .

First, find the slope of the line by using the following formula:

The y-intercept is  since that is given as one of the points on the line.

The line must have the equation .

### Example Question #19 : How To Find The Equation Of A Line

Find the equation of the line that goes through the points  and .

Explanation:

Recall that the slope-intercept form of a line:

,

where  and .

First, find the slope of the line by using the following formula:

Next, find the y-intercept of the line by plugging in  of the points into the semi-completed formula.

Plugging in  yields the following:

Solve for .

The equation of the line is then .

### Example Question #20 : How To Find The Equation Of A Line

Find the equation of the line that goes through the points  and .

Explanation:

Recall that the slope-intercept form of a line:

,

where  and .

First, find the slope of the line by using the following formula:

Next, find the y-intercept of the line by plugging in  of the points into the semi-completed formula.

Plugging in  yields the following:

Solve for .

The equation of the line is then .