Do you know how to identify the slope in an equation? How about the y-intercept?

Take a look at this situation.

**
In this Concept, you will learn how to figure out the slope and the y-intercept by looking at an equation. We will look at this one again at the end of the Concept.
**

### Guidance

We have seen linear equations in function form, have created tables of values and graphs to represent them, looked at their
- and
-intercepts, and studied their slopes. One of the most useful forms of a linear equation is the
**
slope-intercept form
**
which we will be using with standard form in this Concept.

Remember
**
standard form
**
?

**
The standard form of an equation is when the equation is written in
form.
**

This form of the equation allows us to find many possible solutions. In essence, we could substitute any number of values for and and create the value for . When an equation is written in standard form, it is challenging for us to determine the slope and the – intercept.

**
Think back, remember that the
**
**
slope
**

**is the steepness of the line and the**

*– intercept***is the point where the line crosses the – axis.**

**
We can write an equation in a different form than in standard form. This is when
an equation. We call this form of an equation
**
**
slope – intercept form
**

**.**

**
Slope – Intercept Form is
– where
is the slope and
is the
– intercept.
**

Take a look at this graph and equation.

Graph the line

**
Here we can calculate the slope of the line using the rise over the run and see that it is 3. The
– intercept is 1. Notice that we can find these values in our equation too.
**

**
When an equation is in slope – intercept form, we can spot the slope and the
– intercept by looking at the equation.
**

Here is the value of the slope and is the value of the – intercept.

For any equation written in the form
,
is the slope and
is the
-intercept. For that reason,
is called the
*
slope-intercept form.
*
Using the properties of equations, you can write any equation in this form.

**
Because we can use slope – intercept form, we can rewrite equations in standard form into slope – intercept form. Then we can easily determine the slope and
– intercept of each equation.
**

Take a look here.

Write in slope – intercept form. Then determine the slope and the – intercept by using the equation.

**
Now we can determine the slope and the
– intercept from the equation.
**

**
Think back to our work with functions. Remember how we could write a function in function form? Well take a look at function form compared with slope – intercept form.
**

**
Function form
**

**
Slope – Intercept Form
**

**
Yes! The two are the same. These two equations are equivalent!
**

Determine the slope and the y-intercept in each equation.

#### Example A

**
Solution: slope = 1, y-intercept = 4
**

#### Example B

**
Solution: slope = -2, y-intercept = 10
**

#### Example C

**
Solution: slope = 3, y-intercept = 9
**

Now let's go back to the dilemma at the beginning of the Concept.

**
Looking at this equation, you can see that the slope is
and the y-intercept is
.
**

### Vocabulary

- Slope – Intercept Form
- the form of an equation

- Standard Form
- the form of an equation

- Slope
- the steepness of the line, calculated by the ratio of rise over run.

- – Intercept
- the point where a line crosses the axis.

### Guided Practice

Here is one for you to try on your own.

Write this equation in slope-intercept form and then determine the slope and the y-intercept.

**
Given this equation, the slope is 3 and the y-intercept is 2.
**

### Video Review

Converting to Slope-Intercept Form

### Practice

Directions: Look at each equation and identify the slope and the – intercept by looking at each equation. There are two answers for each problem.

Directions: Use what you have learned to write each in slope – intercept form and then answer each question.

- Write this equation in slope – intercept form.
- What is the slope?
- What is the – intercept?
- Write this equation in slope – intercept form.
- What is the slope?
- What is the – intercept?
- Write this equation in slope – intercept form.
- What is the slope?
- What is the – intercept?