# Math Checkup Unit 1 Lesson 3

Topics: Linear function, Fahrenheit, Temperature Pages: 7 (1336 words) Published: August 23, 2013
Checkup: Linear Functions

Answer the following questions using what you've learned from this lesson. Write your responses in the space provided, and turn the assignment in to your instructor.

1. What is the slope of the line in the graph below? Show your work.

To find out the slope, you must first take two separate points on the graph, such as (-5,-1) and (0,1). Then, it’s a simple matter to use the equation [pic] to find the slope:

[pic]= [pic]

2. What is the slope of the line represented by the table of values below? How do you know? |x |y |
|-2 |3 |
|-1 |4.5 |
|0 |6 |
|1 |7.5 |
|2 |9 |

By taking two different (x,y) values from the table and using the [pic] formula, we can easily find the slope. For example, let’s use (-2,3) and (0,6): [pic]= [pic]
3. Which of the following graphs could be the graph of y = - 4x - 5? Circle the letter of your answer(s) and explain your choice(s).

a.

b.

c.

d.

4. Write the equation of the line that passes through the points (3,7) and (-1,2) in:

The slope is [pic]=[pic]=[pic]

a. Point-slope form

y-2=[pic](x+1)

b. Slope-intercept form

y=[pic]x+[pic]

5. What is the slope of a line that is perpendicular to [pic]? Show your work. Answer: A line perpendicular to y=[pic]x would have a slope that’s the reciprocal of the slope to y=[pic]x. So the answer is [pic].

6. Write the equation of a line passing through (0,6) and parallel to the line [pic]. Answer:

y=[pic]x+6

7. Which of the following tables of values could have been generated by a linear function? How do you know?

a.
|x |y |
|-2 | -3 |
|-1 |-5 |
| 0 |-7 |
|1 |-9 |
|2 |-11 |

b.
|x |y |
|-2 |1 |
|-1 |3 |
|0 |6 |
|1 |10 |
|2 |15 |

c.
|x |y |
|-2 |1 |
|-1 |1 |
|0 |1 |
|1 |1 |
|2 |1 |

Table A is a linear function, since it has an even distribution in both its x and y values. Table B is NOT a linear function, since it doesn’t have an even distribution in its y values. Table C is a linear function, since it has an even distribution in both its x and y values.

8. For each table in #7 that could have been generated by a linear function, calculate the slope of the line produced by that function.

The rise over run formula [pic] shows the slope of a function table. Table A has a slope of [pic]= [pic]= -2.
Table C has a slope of [pic]= [pic]= 0.

9. The cost of hosting a dinner in a particular restaurant is given by y = 18.5x + 250, where x is the number of people at the dinner and y is dollars. What is the slope of this function? What does it mean in the context of the problem?

The slope is 18.5. It means that each person that attends costs \$18.50.

10. The cost of hosting a dinner in a particular restaurant is given by y = 18.5x + 250, where x is the number of people at the dinner and y is dollars. What is the y-intercept of this function? What does it mean in the context of the problem?

The y-intercept is 250. This means that you must pay \$250 BEFORE you...