9.5: SlopeIntercept Form
Introduction
Scientists in the Rainforest
The rainforest was such a popular topic of discussion that Mr. Thomas let the students talk about it all week. They loved discussing all of the things that they had seen. One day, they began talking about the scientists and all of the things that they had to carry with them into the rainforest.
“You know, they couldn’t exactly run out to the store to pick something up,” Casey commented.
“Or call for a pizza!” Susan said.
Mr. Thomas once again seized a great opportunity to write the following problem on the board.
A group of backpackers leaves with 84lbs. of food. They plan to eat 11lbs. per day. Use an equation to show on a graph how much food they should have after each day. How long should their food last?
To work on this problem, you will need to know about writing equations involving slope. The food changes per day based on how much the backpackers eat. This lesson will teach you all that you need to know to work on this problem.
What You Will Learn
By the end of this lesson, you will be able to complete the following skills.
 Use a graph to find the slope and
y – intercept of a linear equation given in function form.  Calculate the slopes and
y – intercepts of linear equations in a variety of forms, and recognize slope – intercept form as equivalent to function form.  Graph linear equations given in a variety of forms using slope and
y – intercept.  Solve real – world problems using slope – intercept forms of linear equations.
Teaching Time
I. Use a Graph to Find the Slope and
We have seen linear equations in function form, have created tables of values and graphs to represent them, looked at their
Remember standard form? The standard form of an equation is when the equation is written in
Think back, remember that the slope is the steepness of the line and the
We can write an equation in a different form than in standard form. This is when
Slope – Intercept Form is
Let’s look at an example of the slope – intercept form in action.
Example
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
When an equation is in slope – intercept form, we can spot the slope and the
Here
II. Calculate the Slopes and
For any equation written in the 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
Example
Write
Now we can determine the slope and the
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!
III. Graph Linear Equations Given in a Variety of Forms Using Slope and
Do you see how useful the slopeintercept form,
Example
Graph the line that goes with the equation
First, we can determine that the slope is 1 and the
We can also graph lines in a different form. First, we will need to rewrite them into slope – intercept form. Then we can graph the equation.
Example
Graph the line
First, we rewrite this equation from standard form to slope – intercept form. We do this by using inverse operations.
Now we know that the slope is 3 and the
Now we can look at how linear equations can be found in real – life situations.
IV. Solve Real – World Problems Using Slope – Intercept Forms of Linear Equations
The slopeintercept form allows can be useful in solving many problems in the real world. Let’s look at an example
Example
A store employee gets paid $12.50 per hour plus a weekly bonus of $50 for punctuality. Assuming the employee is on time every day, graph her wages earned. How much would she earn for working 10 hours? 20 hours? 30 hours?
We could use the equation
The graph shows that wages for 10 hours would be $175, for 20 hours $300 and for 30 hours $425.
RealLife Example Completed
Scientists in the Rainforest
Here is the original problem once again. Reread it and then solve Mr. Thomas’ problem using what you have learned in this lesson.
The rainforest was such a popular topic of discussion that Mr. Thomas let the students talk about it all week. They loved discussing all of the things that they had seen. One day, they began talking about the scientists and all of the things that they had to carry with them into the rainforest.
“You know, they couldn’t exactly run out to the store to pick something up,” Casey commented.
“Or call for a pizza!” Susan said.
Mr. Thomas once again seized a great opportunity to write the following problem on the board.
A group of backpackers leaves with 84lbs. of food. They plan to eat 11lbs. per day. Use an equation to show on a graph how much food they should have after each day. How long should their food last?
Solution to Real – Life Example
First, we need to write an equation to represent the food. Use the equation
The graph shows that they have enough food for a little more than seven days.
Vocabulary
Here are the vocabulary words that are found in this lesson.
 Slope – Intercept Form

the form of an equation
y=mx+b
 Standard Form

the form of an equation
Ax+By=C
 Slope
 the steepness of the line, calculated by the ratio of rise over run.

y – Intercept 
the point where a line crosses the
y axis.
Time to Practice
Directions: Look at each equation and identify the slope and the

y=2x+4 
y=3x−2 
y=4x+3 
y=5x−1 
y=12x+2 
y=−2x+4 
y=−3x−1 
y=−13x+5
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
y – intercept?
 Write this equation in slope – intercept form.
 What is the slope?
 What is the
y – intercept?
 Write the following equation in slope – intercept form.
 What is the slope?
 What is the
y – intercept?
Directions: Use what you have learned to solve each problem.
Miguel wants to save $47 for a video game. He received $20 as a gift and gets $4 per week for allowance.
 Write an equation in slopeintercept form that represents this situation.
 Graph the equation.
 How long will it take him to save enough money?
A homeowner wants to reduce the amount of electricity he uses at his house. He finds that he uses 600 watts of power per month. By using energyefficient light bulbs, he decreases his usage by 12 watts per light bulb each month.
 How many energyefficient light bulbs does he need to cut his consumption in half?
 Write an equation in slopeintercept form.