Finding Slope and Intercepts - GED Math

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 .

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

In this equation, and

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

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

Set :

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.

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 .

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:

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

Simply solving, this is

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

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:

The y-intercept is the value of when .

Substitute the value of zero into , and solve for .

Subtract 7 from both sides.

The answer is:

Rewrite the equation in slope-intercept format:

Divide by negative two on both sides. This is also the same as multiplying both sides by negative half.

Rearrange the terms.

The slope is:

The y-intercept is:

The answer is:

Simplify the terms of the equation by distribution.

Subtract the terms.

The equation is now in slope-intercept form, where .

The slope is .

The answer is .

To determine the slope, we will need the equation in slope-intercept form.

Subtract on both sides.

Divide by 9 on both sides.

Split both terms on the right side.

The slope is:

In order to find the y-intercept, we will need to let and solve for .

Subtract from both sides. Do NOT divide by on both sides.

The answer is:

In order to find the x-intercept, we will need to let , and solve for .

Add on both sides.

Divide by five on both sides.

The answer is:

Rewrite the equation in the slope-intercept form , with the slope, as follows:

Subtract from both sides:

Multiply both sides by , distributing on the right:

In the slope-intercept form, the coefficient of is the slope . This is .

To determine the slope, we will need the equation in slope-intercept form.

Divide by six on both sides.

Simplify the right side.

The answer is:

If we look at the following equation

we can see it is written in slope-intercept form. Slope-intercept form is

where m is the slope and b is the y-intercept.

So, given the equation,

we can see -9 is the slope.