High School Math : Pre-Algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #2 : How To Identify A Point In Pre Algebra

If the equation of a line is , what is the y-intercept?

Possible Answers:

Correct answer:

Explanation:

In the slope-intercept form of a line, , the y-intercept when the line intersects the y-axis.

It does this at .

So we plug  in for  in our equation  to give us .

Anything multiplied by  is  so .

Our coordinates for the y-intercept are .

Example Question #3 : How To Identify A Point In Pre Algebra

What is the y-intercept of the line ?

Possible Answers:

Correct answer:

Explanation:

In the standard form of a line  the y-intercept occurs when the line intersects the y-axis.

It does this at 

So we plug  in for  in our equation  to give us .

Anything multiplied by  is  so .

Our coordinates for the y-intercept are .

Example Question #4 : How To Identify A Point In Pre Algebra

What is the slope of a line that is parallel to ?

Possible Answers:

Correct answer:

Explanation:

Parallel lines have the same slope.

If an equation is in point-slope form, , we take the  from our equation and set it equal to the slope of our parallel line.

In this case 

The slope of our parallel line is .

Example Question #1 : How To Identify A Point In Pre Algebra

Define the point based on the coordinate plane.

Number_3

Possible Answers:

Correct answer:

Explanation:

The point resides in quadrant I (the upper right quadrant), so both values must both be positive. The only possible solution is .

Example Question #6 : How To Identify A Point In Pre Algebra

What is the slope of a line that is perpendicular to ?

Possible Answers:

Correct answer:

Explanation:

The slope of a perpendicular lines has the negative reciprocal of the slope of the original line.

If an equation is in point-slope form, , we use the  from our equation as our original slope.

In this case 

First flip the sign to get 

To find the reciprocal you take the integer and make it a fraction by placing a  over it. If it is already a fraction just flip the numerator and denominator.

Do this to make the slope 

The slope of the perpendicular line is .

Example Question #1 : Graphing Lines

What is the slope of the line with the equation ?

Possible Answers:

Correct answer:

Explanation:

In the standard form equation of a line, , the slope is represented by the variable .

In this case the line  has a slope of .

Therefore the answer is .

Example Question #4 : Graphing Lines

What is the slope of the line ?

Possible Answers:

Correct answer:

Explanation:

In the slope-intercept form of a line, , the slope is represented by the variable .

In this case the line

 

has a slope of .

The answer is .

Example Question #5 : Graphing Lines

What is the y-intercept of the line ?

Possible Answers:

Correct answer:

Explanation:

In the slope-intercept form of a line, , the y-intercept is when the line intersects the y-axis.

It does this at .

So we plug  in for  in our equation

 

to give us

Anything multiplied by  is  so

Our coordinates for the y-intercept are .

Example Question #4 : How To Identify A Point In Pre Algebra

What is the slope of a line that is parallel to ?

Possible Answers:

Correct answer:

Explanation:

Parallel lines have the same slope.

If an equation is in slope-intercept form, , we take the  from our equation and set it equal to the slope of our parallel line.

In this case .

The slope of our parallel line is .

Example Question #6 : Graphing Lines

What is the slope of the line that contains the points,  and ?

Possible Answers:

Correct answer:

Explanation:

To find the slope of a line with two points you must properly plug the points into the slope equation for two points which looks like

We must then properly assign the points to the equation as  and .

In this case we will make  our  and  our .

Plugging the points into the equation yields 

Perform the math to arrive at 

The answer is .

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