8th grade · Math · Unit 6 of 11
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.
Minnesota K-12 Academic Standards benchmark: 8.3.7.4; 8.3.7.6 · linear functions in tables, graphs and equations, and their slope and intercepts
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 Minnesota
In the Minnesota K-12 Academic Standards, this is unit 6 of 11 in 8th grade Math, after Scatter Plots & Stories 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
In the relation y = 3x + 6, 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 2
For the relation y = 6x − 1, what is y when x = 8?
answer box
47
Hint: Replace x with 8: 6 × 8 − 1 = 47.
Question 3
The ordered pair (?, -5) is on the line y = 4x − 5. What is the missing x-value?
answer box
0
Hint: Put y = -5 in the equation: -5 = 4x − 5. Undo the subtraction, then divide by 4: x = 0.
Question 4
For the relation y = 6x − 1, what is y when x = 6?
answer box
35
Hint: Replace x with 6: 6 × 6 − 1 = 35.
Question 5
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?
- Yes. Graphs of linear relations must always be joined.
- No. A linear relation cannot be graphed.
- Yes. Every point on the line is a possible number of tickets.
- No. You can only buy a whole number of tickets, so only separate points make sense.
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 6
Which ordered pair is on the graph of y = 4x + 1?
- (4, 17)
- (4, 16)
- (4, 18)
(4, 17)
Hint: Substitute x = 4: 4 × 4 + 1 = 17.