Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1 : How To Graph A Line

Which of the following is the graph of the equation  ?

Possible Answers:

Graph_1

Graph_2

Graph_4

 

Graph_3

 

Graph_5

 

Correct answer:

Graph_1

Explanation:

On the coordinate plane, the graph of an equation of the form  is a vertical line with its -intercept at . Therefore, the graph of  is vertical with -intercept .

Example Question #1 : How To Graph A Line

Which of the following is the graph of the equation  ?

Possible Answers:

Graph_5

Graph_2

Graph_4

Graph_3

None of the other choices are correct.

Correct answer:

None of the other choices are correct.

Explanation:

Since the intercepts are shown on each graph, we find the intercepts of  and compare them.

-intercept:

Set 

The graph goes through . Since none of the graphs shown go through the origin, none of the graphs are correct.

Example Question #1 : How To Graph A Line

Which of the following graphs best represents the following function?

Possible Answers:

None of these

Graph_line_

Graph_cube_

Graph_parabola_

Graph_exponential_

Correct answer:

Graph_line_

Explanation:

This equation describes a straight line with a slope of and a y-intercept of . We know this by comparing the given equation to the formula for a line in slope-intercept form.

The graph below is the answer, as it depicts a straight line with a positive slope and a negative y-intercept.

Graph_line_

Example Question #1 : How To Graph A Line

Which of the following choices is an accurate visual description of the graph of 

Possible Answers:

A line with a positive slope that crosses the -axis at 

A parabola with its vertex at 

A line with a negative slope that crosses the -axis at 

A line with a slope of zero that crosses the -axis at 

A line with a slope of  that crosses the -axis at the origin

Correct answer:

A line with a negative slope that crosses the -axis at 

Explanation:

Though this is a question about a graph, we don't actually have to graph this equation to get a visual idea of its behavior. We just need to put it into slope-intercept form. First, we subtract  from both sides to get

Simplified, this equation becomes 

Remember, this is in  form, where the slope is represented by . Therefore, the slope is negative. The y-intercept is represented by , which is  in this case. So, the line has a negative slope and crosses the -axis at .

Example Question #6 : How To Graph A Line

Which of the following is the graph of the equation  ?

Possible Answers:

Graph_5

Graph_3

 

None of the other choices are correct.

Graph_2

Graph_4

 

Correct answer:

Graph_5

Explanation:

Since the intercepts are shown on each graph, we need to find the intercepts of .

To find the -intercept, set  and solve for :

Therefore the -intercept is .

To find the -intercept, set  and solve for :

Thus the -intercept is .

The correct choice is the line that passes through these two points.

Example Question #7 : How To Graph A Line

Which equation matches the graph of the line shown?

Equation of a line

Possible Answers:

Correct answer:

Explanation:

An equation of a line is made of two parts: a slope and a y-intercept.

The y-intercept is where the function crosses the y-axis which in this problem it is 0.

The slope is determined by the rise of the function over the run which is  , so the function is moving up one and over one.

Therefore your equation is:

, which is simply

Example Question #1 : How To Graph A Point

Which image depicts the point ?

Possible Answers:

Question_8-_incorrect_1

Question_8-_correct

Question_8-_incorrect_3

Question_8-_incorrect_3

Correct answer:

Question_8-_correct

Explanation:

The first number,  indicates how far the point is positioned to the left or right of the origin. Because the number is negative, the point is three units to the LEFT of the origin. The second number indicates how far the point is postioned up or down from the origin. Because the number is positive, the point is located four units above the origin.

Example Question #1 : How To Graph A Point

The length of line segment  is 12 units. If point A is located at , what is a possible location for point B?

Possible Answers:

Correct answer:

Explanation:

To answer this question, we will have to manipulate the distance formula:

To get rid of the square root, we can square both sides:

and plug in the information given in the question.

At this point we can simply plug in the possible values to determine which combination of coordinates will make the equation above true. 

Thus the correct coordinate is,

.

 

 

 

Example Question #3 : How To Graph A Point

Xy

Graph the following 4 points. They will be displayed as (x,y) pairs.

(A)  

(B)  

(C)  

(D)  

Possible Answers:

A2

A1

A3

A4

Correct answer:

A1

Explanation:

To graph these points we just need to remember that the first number is the x value and the second number is the y value. For (A) we have (1,3). So we move one tick over on the positive x-axis. Then from there we move up to the third tick on the y axis:

Aa

If the value is negative we must move in the other direction. So, for all 4 points,

All2

Example Question #4 : How To Graph A Point

What are the coordinates of the point on the given graph?

Graphin a point

Possible Answers:

Correct answer:

Explanation:

When trying to determine coordinates of a point you need to look at the value of x first (how many units left or right the point is, then the y-value (how many up or down it is).

When you look at this point you see that it is moved right 2 units and up 1.

So your coordinates are:

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