# SSAT Upper Level Math : Lines

## Example Questions

### Example Question #11 : Lines

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

Explanation:

In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:

, where  is the slope of the line and  is its -intercept.

Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the -intercept. Plug in known values for  and  taken from the given point into the  equation to find the -intercept:

Multiply:

Subtract  from each side of the equation:

Now that you've solved for , you can plug the given slope  and the -intercept  into the slope-intercept form of the equation of a line to figure out the answer:

### Example Question #12 : Lines

Find the equation of the line that has a slope of  and passes through the point .

Explanation:

In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:

, where  is the slope of the line and  is its -intercept.

Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the -intercept. Plug in known values for  and  taken from the given point into the  equation and solve for  to find the -intercept:

Multiply:

Subtract  from each side of the equation:

Now, we can write the final equation by plugging in the given slope  and the -intercept :

### Example Question #13 : Lines

Find the equation of the line that has a slope of  and passes through the point .

Explanation:

In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:

, where  is the slope of the line and  is its -intercept.

Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the -intercept. Plug in known values for  and  taken from the given point into the  equation and solve for  to find the -intercept:

Multiply:

Add  to each side of the equation:

Now, we can write the final equation by plugging in the given slope  and the -intercept :

### Example Question #14 : Lines

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

Explanation:

In finding the equation of the line given its slope and a point through which it passes, we can use the slope-intercept form of the equation of a line:

, where  is the slope of the line and  is its -intercept.

Since the problem gives us the slope of the line , we just need to use the point that is given to us to find the -intercept. Plug in known values for  and  taken from the given point into the  equation and solve for  to find the -intercept:

Multiply:

Subtract  from both sides of the equation:

Now, we can write the final equation by plugging in the given slope  and the -intercept :

### Example Question #15 : Lines

Find the equation of the line that has a slope of  and passes through the point .

Explanation:

The question gives us both the slope and the -intercept of the line, allowing us to write the following equation by inserting those values into the slope-intercept form of the equation of a line, :

Alternatively, if you did not realize that the problem gives you the -intercept, you could solve it by using the slope-intercept form of the equation of a line. Since the problem gives us the slope of the line , we would just need to use the point that is given to us to find the -intercept. We could plug in the known values for  and  taken from the given point into the  equation and solve for  to find the -intercept:

Multiplying leaves us with:

We could then substitute in the given slope and the -intercept into the  equation to arrive at the correct answer:

### Example Question #16 : Lines

Find the equation of a line that has a slope of  and passes through the point .

Explanation:

The question gives us both the slope and the -intercept of the line. Remember that  represents the slope, and  represents the -intercept to write the following equation:

Alternatively, if you did not realize that the problem gives you the -intercept, you could solve it by using the slope-intercept form of the equation of a line:

, where  is the slope of the line and  is its -intercept.

Since the problem gives us the slope of the line , we would just need to use the point that is given to us to find the -intercept. We could plug in the known values for  and  taken from the given point into the  equation and solve for  to find the -intercept:

Multiplying leaves us with:

.

We could then substitute in the given slope and the -intercept into the  equation to arrive at the correct answer:

### Example Question #17 : Lines

Find the equation of the line that passes through  and .

Explanation:

First, notice that our -intercept for this line is ; we can tell this because one of the points, , is on the -axis since it has a value of  for

Now, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—, and —and then solve for the slope of the line that connects them:

Now, put the two pieces of information together and substitute them into the  equation to solve the problem:

### Example Question #18 : Lines

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

Explanation:

First, notice that our -intercept for this line is ; we can tell this because one of the points, , is on the -axis since it has a value of  for

Now, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—, and —and then solve for the slope of the line that connects them:

Now, put the two pieces of information together and substitute them into the  equation to solve the problem:

### Example Question #19 : Lines

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

Explanation:

First, notice that our -intercept for this line is ; we can tell this because one of the points, , is on the -axis since it has a value of  for

Now, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—, and —and then solve for the slope of the line that connects them:

Now, put the two pieces of information together and substitute them into the  equation to solve the problem:

### Example Question #20 : Lines

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

Explanation:

First, we need to find the slope of the line. We can do that by using the slope equation:

We can substitute in the values of the provided points—, and —and then solve for the slope of the line that connects them:

Next, plug one of the points' coordinates and the slope to the  equation and solve for  to find the -intercept. For this example, let's use the point :

Multiply:

Change  from a whole number to a mixed number with  in the denominator, just like in the fraction :

Subtract  from each side of the equation:

Finally, put the slope and the -intercept into the  equation to arrive at the correct answer: