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Algebra 1 : How to graph a line

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #3301 : Algebra 1

Which of the following is the graph of the equation y = 5 ?

Possible Answers:

Graph_4

Graph_5

Graph_2

Graph_3

Graph_1

Correct answer:

Graph_2

Explanation:

On the coordinate plane, the graph of an equation of the form y = b is a horizontal line with its -intercept at (0,b) . Therefore, the graph of y= 5 is horizontal with -intercept (0,5) .

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Example Question #21 : Graphing

Which of the following is the graph of the equation x = 5 ?

Possible Answers:

Graph_2

Graph_3

Graph_4

Graph_5

Graph_1

Correct answer:

Graph_1

Explanation:

On the coordinate plane, the graph of an equation of the form x = a is a vertical line with its -intercept at (a,0) . Therefore, the graph of x= 5 is vertical with -intercept (5,0) .

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Example Question #22 : Graphing

Which of the following is the graph of the equation y = 5x ?

Possible Answers:

Graph_4

Graph_5

None of the other choices are correct.

Graph_2

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 y = 5x and compare them.

-intercept:

Set x= 0

y = 5x

$y = 5 \cdot 0$

y = 0

The graph goes through (0,0) . Since none of the graphs shown go through the origin, none of the graphs are correct.

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Example Question #23 : Graphing

Which of the following graphs best represents the following function?

f(x)=2x-2

Possible Answers:

None of these

Graph_exponential_

Graph_line_

Graph_parabola_

Graph_cube_

Correct answer:

Graph_line_

Explanation:

f(x)=2x-2

This equation describes a straight line with a slope of and a y-intercept of (0,-2) . We know this by comparing the given equation to the formula for a line in slope-intercept form.

f(x)=mx-b

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

Graph_line_

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Example Question #24 : Graphing

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

2y+3x=1?

Possible Answers:

A parabola with its vertex at $\left ( \frac{1}{3},\frac{1}{2} \right )$

A line with a slope of zero that crosses the -axis at (0,3)

A line with a negative slope that crosses the -axis at $\left ( 0,\frac{1}{2}\right )$

A line with a positive slope that crosses the -axis at $\left ( 0,\frac{1}{2}\right )$

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 $\left ( 0,\frac{1}{2}\right )$

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

2y=-3x+1

Simplified, this equation becomes

$y=-\frac{3}{2}x+\frac{1}{2}$

Remember, this is in y=mx+b form, where the slope is represented by . Therefore, the slope is negative. The y-intercept is represented by , which is $\frac{1}{2}$ in this case. So, the line has a negative slope and crosses the -axis at $\left ( 0,\frac{1}{2}\right )$ .

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Example Question #1 : How To Graph A Line

Which of the following is the graph of the equation y=x-5 ?

Possible Answers:

Graph_2

Graph_3

None of the other choices are correct.

Graph_5

Graph_4

Correct answer:

Graph_5

Explanation:

Since the intercepts are shown on each graph, we need to find the intercepts of y=x-5 .

To find the -intercept, set y = 0 and solve for :

0=x-5

x= 5

Therefore the -intercept is (5,0) .

To find the -intercept, set x= 0 and solve for :

y=0-5

y=-5

Thus the -intercept is (0,-5) .

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

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Example Question #23 : Graphing

Which equation matches the graph of the line shown?

Equation of a line

Possible Answers:

x=1

y=x+1

y=2x

y=1

y=x

Correct answer:

y=x

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 $\frac{1}{1}$ , so the function is moving up one and over one.

Therefore your equation is:

y=x+0 , which is simply y=x

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Algebra 1 : How to graph a line

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #3301 : Algebra 1

Example Question #21 : Graphing

Example Question #22 : Graphing

Example Question #23 : Graphing

Example Question #24 : Graphing

Example Question #1 : How To Graph A Line

Example Question #23 : Graphing

All Algebra 1 Resources

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