Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #13 : Graphing

Picture10

Find the point that corresponds to the following ordered pair:

Possible Answers:

Correct answer:

Explanation:

in order to get to the point , start at the origin and move right  units and up  units.

This is point .

Example Question #3301 : Algebra 1

Picture12

Find the point that corresponds to the following ordered pair:

Possible Answers:

Correct answer:

Explanation:

in order to get to the point , start at the origin and move down  units.

This is point .

Example Question #18 : How To Graph An Ordered Pair

Which ordered pair is plotted on the following graph

Coordinate plane 2

Possible Answers:

Correct answer:

Explanation:

An ordered pair can be looked at like this:

(x-coordinate, y-coordinate)

where the first number represents the x-coordinate and the second number represent the y-coordinate.  

The x-coordinate is simply the position on the x-axis.  The y-coordinate is the position on the y-axis.

 

If we look at a coordinate plane, we can see where the x- and the y-axes are located.

Blank coordinate plane

The x-axis is horizontal (going left to right) and the y-axis is vertical (going up and down).

Now, when we graph the ordered pair , we locate  on the x-axis.

Coordinate plane  2

In this example, the y-coordinate is . From the current position, we locate  on the y-axis.  

Coordinate plane  2 4

This is where we plot the point

Coordinate plane 2

Example Question #19 : How To Graph An Ordered Pair

Picture11

Find the point that corresponds to the following ordered pair:

Possible Answers:

Correct answer:

Explanation:

In order to get to the point , start at the origin and move left  units and up  units.

This is point .

Example Question #1 : How To Graph A Line

Which of the following is the graph of the equation  ?

Possible Answers:

Graph_2

Graph_3

Graph_4

Graph_1

Graph_5

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 #21 : Graphing

Which of the following is the graph of the equation  ?

Possible Answers:

Graph_2

Graph_4

 

Graph_5

 

Graph_3

 

Graph_1

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 #22 : Graphing

Which of the following is the graph of the equation  ?

Possible Answers:

Graph_2

None of the other choices are correct.

Graph_5

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 #23 : Graphing

Which of the following graphs best represents the following function?

Possible Answers:

Graph_line_

Graph_cube_

None of these

Graph_exponential_

Graph_parabola_

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 #24 : Graphing

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

Possible Answers:

A parabola with its vertex at 

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

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

A line with a negative slope 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 #2 : How To Graph A Line

Which of the following is the graph of the equation  ?

Possible Answers:

Graph_3

 

Graph_2

Graph_5

Graph_4

 

None of the other choices are correct.

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.

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