Linear Equations in Two Variables
Reading to Learn Mathematics
Pre-Activity
How can the relationship between actual temperatures and windchill temperatures
be a function?
Do the activity at the top of page 369 in your textbook. Write your answers below.
a. On grid paper, graph the temperatures as ordered pairs (actual, windchill).
b. Describe the relationship between the two temperature
scales. S
ample answer:
c. When the actual temperature is 220°F, which is the best estimate for the windchill: 246°F, 228°F, or 0°F? Explain. 246°F; when th
Reading the Lesson 1–2. See students’ work.
Write a definition and give an example of each new vocabulary word or phrase.
Vocabulary | Definition | Example |
1. function | ||
2. vertical line test |
3. For a relation to be a function, each element in the must have only one corresponding element in the .
4. Explain what is meant by the phrase “distance is a function of time.” Sample answer:
How far something travels depends on how much time elapses.
Helping You Remember
5. You have learned various ways to determine whether a relation is a function. Choose which method is the easiest for you to use, then write a few sentences explaining how that method relates to the other methods.
Skills Practice
Linear Equations in Two
Variables
Find four solutions of each equation. Write the solutions as ordered pairs.
1. y = 8x - 4 | 2. y = -x + 12 | 3. 4x - 4y = 24 |
4. x - y = -15 | 5. y =7x - 6 | 6. y= 5 -3x + 8 |
7. y =12 | 8. 4x - 2y = 0 | 9. 4x - y = 4 |
Graph each equation by plotting ordered pairs.
Practice
Linear Equations in Two Variables
Find four solutions of each equation. Write the solutions as ordered pairs.
1. y = x - 5 | 2. y = -7 | 3. y = -3x + 1 |
4. x - y = 6 | 5. y = 2x + 4 | 6. 7x - y = 14 |
Graph each equation by plotting ordered pairs.
COOKING For Exercises 13–15, use the following information.
Kirsten is making gingerbread cookies using her grandmother’s recipe and needs to convert grams to ounces. The equation y 5 0.04x describes the approximate number of ounces y in x grams.
13. Find three ordered pairs of values that satisfy this equation.ample answer: (100, 4), (200, 8), (300, 12)
14. Draw the graph that contains these points.
15. Do negative values of x make sense in this case? Explain.
Reading to Learn Mathematics
Linear Equations in Two Variables
Pre-Activity
How can linear equations represent a function?
Do the activity at the top of page 375 in your
textbook. Write your answers below.
a. Complete the table to find the cost
Number of Cans (x) |
1.50x |
Cost (y) |
1 | 1.50(1) | 1.50 |
2 | ||
3 | ||
4 |
b. On grid paper, graph the of 2, 3, and 4 cans of peaches. ordered pairs (number, cost). Then draw a line through the points.
c. Write an equation representing the relationship between number of cans x and cost y.
Reading the Lesson
Write a definition and give an example of the new vocabulary phrase.
1.
Vocabulary | Definition | Example |
linear equation |
2. Determine whether each equation below is linear or nonlinear and explain why.
a. y = x + 1
b. y = x^{2} + 1
c. xy = 4
3. Solutions of a linear equation are that make the equation true.
Helping You Remember
4. Work with one of your classmates translating linear equations into English. First, each of you should write a linear equation. Then trade equations and take turns reading the equations in everyday words. Second, each of you should describe a line in terms of its x and y values. Trade sentences and translate them into linear equations.