### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #1 : Equations Of Lines

Give the equation of a line that passes through the point and has slope 1.

**Possible Answers:**

**Correct answer:**

We can use the point slope form of a line, substituting .

or

### Example Question #2 : Equations Of Lines

A line can be represented by . What is the slope of the line that is perpendicular to it?

**Possible Answers:**

**Correct answer:**

You will first solve for Y, to get the equation in form.

represents the slope of the line, which would be .

A perpendicular line's slope would be the negative reciprocal of that value, which is .

### Example Question #3 : Equations Of Lines

Find the equation the line goes through the points and .

**Possible Answers:**

**Correct answer:**

First, find the slope of the line.

Now, because the problem tells us that the line goes through , our y-intercept must be .

Putting the pieces together, we get the following equation:

### Example Question #4 : Equations Of Lines

A line passes through the points and . Find the equation of this line.

**Possible Answers:**

**Correct answer:**

To find the equation of a line, we need to first find the slope.

Now, our equation for the line looks like the following:

To find the y-intercept, plug in one of the given points and solve for . Using , we get the following equation:

Solve for .

Now, plug the value for into the equation.

### Example Question #5 : Equations Of Lines

What is the equation of a line that passes through the points and ?

**Possible Answers:**

**Correct answer:**

First, we need to find the slope of the line.

Next, find the -intercept. To find the -intercept, plug in the values of one point into the equation , where is the slope that we just found and is the -intercept.

Solve for .

Now, put the slope and -intercept together to get

### Example Question #6 : Equations Of Lines

Examine the above diagram. What is ?

**Possible Answers:**

**Correct answer:**

Use the properties of angle addition:

### Example Question #7 : Equations Of Lines

Are the following two equations parallel?

**Possible Answers:**

Yes

No

**Correct answer:**

Yes

When two lines are parallal, they must have the same slope.

Look at the equations when they are in slope-intercept form, where b represents the slope.

We must first reduce the second equation since all of the constants are divisible by .

This leaves us with . Since both equations have a slope of , they are parallel.

### Example Question #8 : Equations Of Lines

Reduce the following expression:

**Possible Answers:**

**Correct answer:**

For this expression, you must take each variable and deal with them separately.

First divide you two constants .

Then you move onto and when you divide like exponents you must subtract the exponents leaving you with .

is left by itself since it is already in a natural position.

Whenever you have a negative exponential term, you must it in the denominator.

This leaves the expression of .

### Example Question #9 : Equations Of Lines

Give the equation of a line that passes through the point and has an undefined slope.

**Possible Answers:**

**Correct answer:**

A line with an undefined slope has equation for some number ; since this line passes through a point with -coordinate 4, then this line must have equation

### Example Question #1 : Equations Of Lines

Give the equation of the line through and .

**Possible Answers:**

**Correct answer:**

First, find the slope:

Apply the point-slope formula:

Rewriting in standard form: