Algebra 1 : How to graph a line

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_3

Graph_1

Graph_2

Graph_5

Graph_4

Correct answer:

Graph_2

Explanation:

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

Example Question #2 : How To Graph A Line

Which of the following is the graph of the equation  ?

Possible Answers:

Graph_3

 

Graph_1

Graph_5

 

Graph_4

 

Graph_2

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 #3 : How To Graph A Line

Which of the following is the graph of the equation  ?

Possible Answers:

Graph_5

Graph_2

None of the other choices are correct.

Graph_4

Graph_3

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 #4 : How To Graph A Line

Which of the following graphs best represents the following function?

Possible Answers:

Graph_line_

None of these

Graph_parabola_

Graph_exponential_

Graph_cube_

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 #5 : 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 slope of  that crosses the -axis at the origin

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

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

 

Graph_2

None of the other choices are correct.

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

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