# SSAT Upper Level Math : How to find the equation of a line

## Example Questions

### Example Question #1 : How To Find The Equation Of A Line

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

Explanation:

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

or

### Example Question #1 : How To Find The Equation Of A Line

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

Explanation:

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 : How To Find The Equation Of A Line

Find the equation the line goes through the points  and .

Explanation:

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 #1 : How To Find The Equation Of A Line

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

Explanation:

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 #2 : How To Find The Equation Of A Line

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

Explanation:

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 #191 : Ssat Upper Level Quantitative (Math)

Examine the above diagram. What is  ?

Explanation:

Use the properties of angle addition:

### Example Question #1 : Equations Of Lines

Are the following two equations parallel?

Yes

No

Yes

Explanation:

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 #193 : Ssat Upper Level Quantitative (Math)

Reduce the following expression:

Explanation:

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 #1 : How To Find The Equation Of A Line

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

Explanation:

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 #2 : How To Find The Equation Of A Line

Give the equation of the line through  and .