## Linear Function Word Problems

#### Aligned To Common Core Standard:

**High School Statistics** - HSS-ID.B.6a

What is a Linear Function? Linear functions are those algebraic functions which have a graphical figure of straight lines consisting of unique values on their slopes and y-intercept. In other words, a linear function is an equation which is either a constant or a product of a constant whose highest power is 1. For instance, the perfect example of a linear equation is y=mx+b, while the equation is called the slope-intercept form. This equation meets all the criteria of a linear function, i.e. two variables in the form of x and y, while also having two constants m and b. in the equation you can also see that the highest power of the variables is 1. A series of worksheets and lessons that help students tackle word problems that include functions that can be graphed to form straight lines.

### Printable Worksheets And Lessons

- John's Rice Buying Step-by-step Lesson- Create an equation to represent the rate at which John purchases rice.
- Guided Lesson - Nail growth, borrowing bicycles, and a leaky water faucet.
- Guided Lesson Explanation - I somewhat shot through the explanation quickly.
- Practice Worksheet - Baby's hair growth, filling water tanks, and the Earth's temperature.
- Matching Worksheet - Find the graph of each situation that is explained to you.

#### Homework Sheets

You would not imagine how often linear functions are found in everyday problems. These problems will give you a glimpse.

- Homework 1 - Determine the equation and represent the function that defines the cost of corn based on weight.
- Homework 2 - It has been observed that a particular hair's growth is directly proportional to time. When we last measured, the hair was 5 cm and 6.5 cm exactly one week later. If the hair continues to grow at this rate, determine the function that represents the hair's growth and graph it.
- Homework 3 - Aryan wants to borrow a car. He borrows a car from Frieda. The car rental charge is $12 per day plus $0.40 per mile travelled. Determine the equation of the line that represents the daily cost by the number of miles travelled and graph it. If a total of 100 miles were travelled in two days, how much is the rental cost?

#### Practice Worksheets

When the graph answers are printed in pure grayscale, they come out great!

- Practice 1 - Henry has been measuring the length of his baby's nail. The first time it was 2 cm long and after one month it was 2.2 cm long. If the nail continues to grow at this rate, determine the function that represents the nail growth and graph it.
- Practice 2 - Denzel is making cups of homemade hot chocolate at the rate of 7 cups in an hour. Create a hypothetical table of values for time and capacity. Determine the equation that represents the function and state it graphically.
- Practice 3 - Goldie has purchased five pounds of copper tubing from the hardware store for $100. Determine the equation and represent the function that defines the cost of copper tubing based on weight.

#### Math Skill Quizzes

The first quiz will tell you if the kids have the concept. The third quiz will tell you if they mastered the skill.

- Quiz 1 - Gerald has purchased four pairs of sticks from the market for $10. Determine the function that defines the cost of one pair of sticks based on quantity.
- Quiz 2 - Eva writes 3 pages in an hour. Determine the equation that represents the function and state it graphically.
- Quiz 3 - It has been observed that a particular plant's growth is directly proportional to time. When we last measured, the plant was 4 cm and 4.6 cm exactly one week later. If the plant continues to grow at this rate, determine the function that represents the plant's growth and graph it.

### Tips for Solving Linear Functions

As we know these algebraic statements can be used to form lines. There is a pretty straight forward strategy you can use when approaching these types of problems and it falls down into three steps. The first step is to swap out the f(x) value and fit into the problem. The next step is to get the variable alone and by itself. While I say this is the next step, it can take you several moves to make it happen. It usually starts with countering the constant value. You can to this by just applying the opposite operation to both sides of the equation. After that you will need to continue through the problem by countering a series of operations the end goal is the get that variable by itself equal to something else. The last step is often to simplify what ever you are left with. This can sometimes be finishing out an exponent, combining a series of operations, or just simplifying a fraction or series of them.