### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #11 : Lines

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

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

, 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 .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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

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:

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