### All Algebra 1 Resources

## Example Questions

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

Which of the following is the graph of the equation ?

**Possible Answers:**

**Correct answer:**

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:**

**Correct answer:**

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:**

None of the other choices are correct.

**Correct answer:**

None of the other choices are correct.

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:**

None of these

**Correct answer:**

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 #5 : How To Graph A Line

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 that crosses the -axis at the origin

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

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:**

None of the other choices are correct.

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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