Name: _____________________
Math 8 PRACTICE Test: Understanding Linear Functions and Slope
1. Complete the table and graph. State whether the function is linear or nonlinear.
y = 2x - 5
x
-2
-1
0
1
2
2x - 5
y
(x, y)
Is the relationship linear or nonlinear? _______________
Determine if these graphs represent linear relationships.
2.
3.
Determine whether these equations represent a LINEAR relationship. EXPLAIN your
answer.
4. y = -4x - 8
5. y = 3x2 + 5
6. 2y +
7
𝑥
= 14
Determine if these tables represent linear relationships. EXPLAIN your answer!
7.
Explanation:
x
2
4
5
6
y
10
9
8
7
Math 8: Understanding Linear Functions and Slope
8.
x
1
3
4
5
Explanation:
y
4
12
16
20
9.
x
-5
-4
-3
-2
Explanation:
y
2
4
6
8
10 – 15. Find the slope from the graphs. Make sure your answers are in simplest
form.
Math 8: Understanding Linear Functions and Slope
Find the slope using the slope formula (SHOW YOUR WORK using the slope
formula!). Make sure your answers are in simplest form.
16. (2, 5), (3, 6)
17. (6, 1), (-6, 1)
18. (4, 6), (4, 8)
19. (5, 2), (5, -2)
20. (2, 5), (-3, -5)
21. (9, 8), (7, -8)
22. Carla has already written 10 pages of a novel. She plans to write 15 additional pages
per month until she is finished.
Write an equation to find the total number of pages P
written after any number of months m.
Graph the equation on the grid to the right.
What is the slope of this graph? ______
What is the y-intercept of this graph? _______
In a complete sentence, explain what the slope means in the context of the problem.
In a complete sentence, explain what the y-intercept means in the context of the problem.
Math 8: Understanding Linear Functions and Slope
23. A tractor has a gas tank that holds 14 gallons of gas. It uses gas at a rate of about
2.5 gallons each hour. You start plowing with a full tank of gas.
Complete the table.
Hours (x)
Gallons of Gas Left (y)
0
1
2
3
4
Write an equation that shows how much gas (y) will be in the tank after each hour (x) of
use.
In a complete sentence, explain what the slope means in the context of the problem.
In a complete sentence, explain what the y-intercept means in the context of the problem.
Write a linear equation in slope-intercept form to model each situation. Then, EXPLAIN
the meaning of the slope and y-intercept in the context of the problem.
24. A computer technician charges $75 for a consultation plus $35 per hour.
25. The population of Pine Bluff is 6791 and is decreasing at the rate of 7 per year.
26. A video store charges $10 for a rental card plus $2 per rental.
27. A Norfolk pine is 18 inches tall and grows at a rate of 1.5 feet per year.
29. An airplane at an altitude of 3000 feet descends at a rate of 500 feet per mile.
30. Graph the equation described and then explain the meaning
of the slope and y-intercept in the context of the problem.
The number of delivered toys T is three times the
total number of crates c.