# Algebra 1 : Functions and Lines

## Example Questions

### Example Question #1 : How To Graph A Line

Which of the following is the graph of the equation  ?

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  ?

None of the other choices are correct.

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?

None of these

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.

### Example Question #1 : How To Graph A Line

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

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

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  ?

None of the other choices are correct.

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?

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.

, which is simply

### Example Question #1 : How To Graph A Point

Which image depicts the point ?

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?

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

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

(A)

(B)

(C)

(D)

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:

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

### Example Question #4 : How To Graph A Point

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