8th grade · Math · Unit 9 of 17
Tables, Graphs & Linear Relations
Find missing values in y = mx + b
What your child practices
Using an equation like y = 3x + 2 to build a table of values, find a missing x or y, and describe how the variables change together.
Arizona Academic Standards learning standard: 8.F.A.3; 8.F.B.4 · linear functions of the form y = mx + b, their tables and graphs
How we explain it
Children can open this short lesson before they practice.
- A table pairs each x with a y.
- Plot each pair as a point. A straight line means a linear relation.
- Look at how y changes each time x goes up by 1.
Example: x = 0, 1, 2 gives y = 3, 5, 7. What is y when x = 3? y goes up by 2 each time. 7 + 2 = 9. Answer: 9
Tables, Graphs & Linear Relations in Arizona
In the Arizona Academic Standards, this is unit 9 of 17 in 8th grade Math, after Angle Detective and before Equations with Brackets.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Source: Arizona Department of Education
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
A graph shows the number of team shirts bought (1, 2, 3 and so on) and the total cost. Should the points be joined with a line?
- No. You can only buy a whole number of team shirts, so only separate points make sense.
- Yes. Every point on the line is a possible number of team shirts.
- No. A linear relation cannot be graphed.
- Yes. Graphs of linear relations must always be joined.
No. You can only buy a whole number of team shirts, so only separate points make sense.
Hint: Discrete data counts whole items, so values between the points are not possible.
Question 2
Which equation matches the table of values?
x y 1 7 2 11 3 15 4 19 - y = 3x + 4
- y = 5x + 3
- y = 4x − 3
- y = 4x + 3
y = 4x + 3
Hint: Test the first row: x = 1 gives y = 7. Only y = 4x + 3 works for every row.
Question 3
The table shows a linear relation. What number goes in place of the ?
Table of values x y 0 -5 1 -2 2 1 3 4 4 ? answer box
7
Hint: Look at how y changes each time x goes up by 1. It changes by 3, so y = 7 when x = 4.
Question 4
For the relation y = 3x + 6, what is y when x = -1?
answer box
3
Hint: Replace x with -1: 3 × (-1) + 6 = 3.
Question 5
Which ordered pair is on the graph of y = 2x + 4?
- (1, 7)
- (1, 2)
- (1, 6)
- (1, 5)
(1, 6)
Hint: Substitute x = 1: 2 × 1 + 4 = 6.
Question 6
For the relation y = 2x + 7, what is y when x = -1?
answer box
5
Hint: Replace x with -1: 2 × (-1) + 7 = 5.