### All GED Math Resources

## Example Questions

### Example Question #1 : Finding Slope And Intercepts

Find the slope and y-intercept of the line depicted by the equation:

**Possible Answers:**

**Correct answer:**

The equation is written in slope-intercept form, which is:

where is equal to the slope and is equal to the y-intercept. Therefore, a line depicted by the equation

has a slope that is equal to and a y-intercept that is equal to .

### Example Question #1 : Finding Slope And Intercepts

Find the slope and y-intercept of the line that is represented by the equation

**Possible Answers:**

**Correct answer:**

The slope-intercept form of a line is: , where is the slope and is the y-intercept.

In this equation, and

### Example Question #1 : Finding Slope And Intercepts

The grade of a road is defined as the slope of the road expressed as a *percent *as opposed to a fraction or decimal.

A road is graded so that for every 40 feet of horizontal distance, the road rises 6 feet. What is the grade of the road?

**Possible Answers:**

**Correct answer:**

The slope is the ratio of the vertical change (rise) to the horizontal change (run), so the slope of the road, as a fraction, is . Multiply this by 100% to get its equivalent percent:

This is the correct choice.

### Example Question #4 : Finding Slope And Intercepts

Refer to above red line. What is its slope?

**Possible Answers:**

**Correct answer:**

Given two points, , the slope can be calculated using the following formula:

Set :

### Example Question #1 : Finding Slope And Intercepts

What is the slope and y-intercept of the following line?

**Possible Answers:**

**Correct answer:**

Convert the equation into slope-intercept form, which is , where is the slope and is the y-intercept.

### Example Question #1 : Finding Slope And Intercepts

What is the slope of the line perpendicular to ?

**Possible Answers:**

**Correct answer:**

In order to find the perpendicular of a given slope, you need that given slope! This is easy to compute, given your equation. Just get it into slope-intercept form. Recall that it is

Simplifying your equation, you get:

This means that your perpendicular slope (which is *opposite* *and reciprocal*) will be .

### Example Question #1 : Finding Slope And Intercepts

What is the equation of a line with a slope perpendicular to the line passing through the points and ?

**Possible Answers:**

**Correct answer:**

First, you should solve for the slope of the line passing through your two points. Recall that the equation for finding the slope between two points is:

For your data, this is

Now, recall that perpendicular slopes are *opposite and* reciprocal. Therefore, the slope of your line will be . Given that all of your options are in slope-intercept form, this is somewhat easy. Remember that slope-intercept form is:

is your slope. Therefore, you are looking for an equation with

The only option that matches this is:

### Example Question #1 : Finding Slope And Intercepts

What is the x-intercept of ?

**Possible Answers:**

No x-intercept

**Correct answer:**

Remember, to find the x-intercept, you need to set equal to zero. Therefore, you get:

Simply solving, this is

### Example Question #1 : Finding Slope And Intercepts

Find the slope of the line that has the equation:

**Possible Answers:**

**Correct answer:**

Step 1: Move x and y to opposite sides...

We will subtract 2x from both sides...

Result,

Step 2: Recall the basic equation of a line...

, where the coefficient of y is .

Step 3: Divide every term by to change the coefficient of y to :

Step 4: Reduce...

Step 5: The slope of a line is the coefficient in front of the x term...

So, the slope is

### Example Question #81 : Linear Algebra

Find the slope of the following equation:

**Possible Answers:**

**Correct answer:**

In order to find the slope, we will need the equation in slope-intercept form.

Distribute the negative nine through the binomial.

The slope is:

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