Slope-Intercept Form - GED Math

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

Below are the steps to get the equation into slope-intercept form.

First, we need to find the slope of the above line.

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

Set :

Second, we note that the -intercept is the point .

Therefore, in the slope-intercept form of a line, we can set and :

There are two ways that you can find the y-intercept for an equation. You could substitute in for . This would give you:

Simplifying, you get:

However, another way to do this is by finding the slope-intercept form of the line. You do this by solving for :

Just divide everything by :

Remember that the slope-intercept form gives you the intercept as the final constant. Hence, it is as well!

There are two ways that you can find the y-intercept for an equation. You could substitute in for . This would give you:

Simplifying, you get:

However, another way to do this is by finding the slope-intercept form of the line. You do this by solving for . Indeed, this is very, very easy. Recall that the slope intercept form is:

This means that, as written, your equation obviously has . You don't even have to do all of the simplification!

In order to figure this out, you should use your slope-intercept formula. Remember that the y-intercept is the place where is zero. Therefore, the point gives you your y-intercept. It is . Now, to find the slope, recall the slope equation, namely:

For your points, this would be:

This is your slope.

Now, recall that the point-slope form of an equation is:

, where is your slope and is your y-intercept

Thus, your equation will be:

In order to compute the slope of a line, there are several tools you can use. For this question, try to use the slope-intercept form of a line. Once you get the equation into this form, you basically can "read off" the slope right from the equation! Recall that the slope-intercept form of an equation is:

Now, looking at each of your options, you know that you can eliminate two immediately, as their slopes obviously are not :

The next is almost as easy:

When you solve for , your coefficient value for is definitely not equal to :

Next, is not correct either. When you start to solve, you should notice that will always have a negative coefficient. This means that it certainly will not become when you finish out the simplification.

Thus, the correct answer is:

Really, all you have to pay attention to is the term. First, you will subtract from both sides:

Then, just divide by , and you will have !

In order to rewrite the equation in slope-intercept form, we will need to multiply the reciprocal of the coefficient in front of y.

Simplify both sides.

The answer is:

The slope-intercept form is:

Subtract on both sides.

Divide by negative six on both sides.

Simplify both sides.

The answer is:

Slope intercept form is .

Add on both sides.

Multiply by three on both sides.

The answer is:

The slope-intercept form is defined as .

The equations in the answer choices are not in slope-intercept form.

The equation is not linear.

The equation is in standard form.

The answer is:

The slope-intercept form is:

Add on both sides.

Simplify both sides of the equation.

The answer is:

The slope intercept form is:

The equation must be written in terms of .

The term cannot be in the denominator of a fraction, or it will not be linear.

The answer is:

The slope intercept form is:

Divide both sides by three.

Add 2 on both sides.

The answer is:

Distribute the right side.

Divide both sides by two.

Simplify both sides.

The answer is:

Slope-intercept must be in the form:

Subtract from both sides.

Rewrite the equation.

The answer is:

Distribute the five on the right side.

Add three on both sides.

The answer is:

The slope-intercept format is:

Add on both sides.

Subtract 6 from both sides.

Divide by 3 on both sides.

The answer is:

The slope intercept form is:

To isolate the y-variable, simply add on both sides.

The answer is:

To write the equation in slope intercept form, first recall the general form for slope intercept.

where represents the slope and represents the y-intercept.

Given the equation in this question,

first subtract the .

Now to isolate multiply both sides by three.

Distribute the three to all parts within the parentheses.