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

## Example Questions

### Example Question #21 : 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:

Since the slope of the line is undefined, this must be just a vertical line with the equation .

### Example Question #22 : How To Find The Equation Of A Line

Find the equation of the line that passes 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:

Since the slope is , the line is a horizontal line with the equation .

### Example Question #23 : How To Find The Equation Of A Line

Find the equation of the line that passes 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 #24 : How To Find The Equation Of A Line

Find the equation of the line that passes 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 #51 : Other Lines

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

Explanation:

Start by finding the slope of the line.

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

, where  is the slope and  is the point.

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

, where  is the slope and  is the y-intercept.

### Example Question #52 : Other Lines

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

Explanation:

Start by finding the slope of the line.

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

, where  is the slope and  is the point.

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

, where  is the slope and  is the y-intercept.

### Example Question #53 : Other Lines

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

Explanation:

Start by finding the slope of the line.

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

, where  is the slope and  is the point.

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

, where  is the slope and  is the y-intercept.

### Example Question #54 : Other Lines

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

Explanation:

Start by finding the slope of the line.

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

, where  is the slope and  is the point.

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

, where  is the slope and  is the y-intercept.

### Example Question #55 : Other Lines

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

Explanation:

Start by finding the slope of the line.

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

, where  is the slope and  is the point.

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

, where  is the slope and  is the y-intercept.

### Example Question #56 : Other Lines

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