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.
Alabama Course of Study content standard: 8.14; 8.16 · 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 Alabama
In the Alabama Course of Study, 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.
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
For the relation y = 2x + 9, what is y when x = 1?
answer box
11
Hint: Replace x with 1: 2 × 1 + 9 = 11.
Question 2
In the relation y = 3x − 3, by how much does y change each time x increases by 1?
answer box
3
Hint: The number multiplying x is 3, so y changes by 3 for each step of 1 in x.
Question 3
The ordered pair (?, 39) is on the line y = 5x + 9. What is the missing x-value?
answer box
6
Hint: Put y = 39 in the equation: 39 = 5x + 9. Undo the addition, then divide by 5: x = 6.
Question 4
A graph shows the number of tickets bought (1, 2, 3 and so on) and the total cost. Should the points be joined with a line?
- No. A linear relation cannot be graphed.
- No. You can only buy a whole number of tickets, so only separate points make sense.
- Yes. Every point on the line is a possible number of tickets.
- Yes. Graphs of linear relations must always be joined.
No. You can only buy a whole number of tickets, so only separate points make sense.
Hint: Discrete data counts whole items, so values between the points are not possible.
Question 5
Which equation matches the table of values?
x y 1 7 2 9 3 11 4 13 - y = 3x + 5
- y = 5x + 2
- y = 2x − 5
- y = 2x + 5
y = 2x + 5
Hint: Test the first row: x = 1 gives y = 7. Only y = 2x + 5 works for every row.
Question 6
Which ordered pair is on the graph of y = 3x + 6?
- (6, 18)
- (6, 24)
- (6, 23)
- (6, 25)
(6, 24)
Hint: Substitute x = 6: 3 × 6 + 6 = 24.