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

Study concepts, example questions & explanations for SSAT Upper Level Math

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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.

Possible Answers:

Correct answer:

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?

Possible Answers:

Correct answer:

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 #2 : How To Find The Equation Of A Line

Find the equation the line goes through the points  and .

Possible Answers:

Correct answer:

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 #4 : How To Find The Equation Of A Line

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

Possible Answers:

Correct answer:

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 #3 : How To Find The Equation Of A Line

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

Possible Answers:

Correct answer:

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 #4 : How To Find The Equation Of A Line

Lines

Examine the above diagram. What is  ?

Possible Answers:

Correct answer:

Explanation:

Use the properties of angle addition:

Example Question #5 : Equations Of Lines

Are the following two equations parallel?

Possible Answers:

Yes

No

Correct answer:

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 #8 : How To Find The Equation Of A Line

Reduce the following expression:

Possible Answers:

Correct answer:

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 #5 : How To Find The Equation Of A Line

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

Possible Answers:

Correct answer:

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 #6 : How To Find The Equation Of A Line

Give the equation of the line through  and .

Possible Answers:

Correct answer:

Explanation:

First, find the slope:

Apply the point-slope formula:

Rewriting in standard form:

 

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