1.3.1: Creating and Graphing Linear Equations in Two Variables

1.3.1: Creating and Graphing Linear Equations in Two Variables

1

Lesson 2.6 Creating and Graphing

Linear Equations in Two Variables

Concept: Graphing Linear Equations

EQ: How do I create and graph a linear equation in two variables from a word problem? (Standard CED.2)

Vocabulary: Slope, Y-Intercept, Independent & Dependent Variable


2

Creating & Graphing Linear Equations

1. Read the problem statement carefully.2. Look for the information given and make a list or

underline the known quantities.3. Determine which information tells you the rate of change,

or the slope, m. Look for words such as each, every, per, or rate.

4. Determine which information tells you the y-intercept, or b. This could be an initial or starting value, a flat fee, and so forth.

5. Substitute the slope and y-intercept into the linear equation formula, y = mx + b.

6. Set up the coordinate plane and identify the independent and dependent variables.

7. Graph the equation by using the slope and y-intercept or by making a table of values.

Guided Practice - Example 1A taxi company in Atlanta charges $2.50 for a ride plus $2 for every mile driven. Write and graph the equation that models the taxi company’s total fees.

1. Read the problem.2. Determine the known quantities.3-4. Identify the slope and the y-intercept.

slope _____ y-intercept ______5. Substitute the slope and y-intercept into the equation y = mx + b, where m is the slope and b is the y- intercept. _____________


3


4

Example 1, continued6. Set up the coordinate

plane and identify the independent and dependent variables.

7. Graph the equation using the slope and y-intercept. Plot the y-intercept first and then use the slope to find the second point.

Equation:y = 2x + 2.50

Guided Practice - Example 2

Matthew receives a base weekly salary of $300 plus commission of $50 for each vacuum he sells. Write and graph the equation that models his weekly earnings.

Slope: ________________ y-intercept: _____________

Equation: ___________________


5


6

Example 2, continued

Use the y-intercept to help you graph your first point. Use the slope to help you find your second point.

Vacuums sold

You Try!

A 12-inch candle burns at a rate of 2 inches per hour. Write and graph the equation that models the height of the candle over time.

1. Read the problem.

2. Determine the known quantities.

3-4. Identify the slope and the y-intercept.

slope _____ y-intercept ______

5. Substitute the slope and y-intercept into the equation

y = mx + b, where m is the slope and b is the

y- intercept.

_____________


7


8

You Try , continued

Use the y-intercept to help you graph your first point. Use the slope to help you find your second point.

Hours


A water company charges a monthly fee of $6.70 plus a usage fee of $2.60 per 1,000 gallons used. Write and graph the equation that models the water company’s total fees.

Slope: ________________ y-intercept: _____________

Equation: ___________________


9


10


Graph the equation by making a table of values.

x y

0

5

7


A local convenience store owner spent $10 on pencils to resell at the store. Write and graph the equation of the store’s revenue if each pencil sells for $0.50.

Slope: _____________ y-intercept: _____________

Equation: ___________________


11


12



x y

0

2

4

You Try!

Maddie borrowed $1,250 from a friend to buy a new TV. Her friend doesn’t charge any interest, and Maddie makes $40 payments each month. Write and graph the equation that models the money Maddie owes.

1. Read the problem.

2. Determine the known quantities.

3-4. Identify the slope and the y-intercept.

slope _____ y-intercept ______

5. Substitute the slope and y-intercept into the equation

y = mx + b, where m is the slope and b is the

y- intercept.

_____________1.3.1: Creating and Graphing Linear Equations in Two Variables

13


14

You Try, continued


x y

0

6

21

Documents

1.3.1: Creating and Graphing Linear Equations in Two Variables