7th grade · Math · Unit 17 of 22
Linear Relations
Patterns in tables and graphs
What your child practices
Finding the rule behind growing patterns, writing expressions like 3n + 2, and connecting tables, graphs and real situations such as rental costs.
Texas Essential Knowledge and Skills (TEKS) teks student expectation: 7.7 · linear relationships in words, tables, graphs and equations of the form y = mx + b
How we explain it
Children can open this short lesson before they practice.
- A table pairs each x with a y.
- Look for how y changes each time x goes up by 1.
- Use that change to carry the pattern on.
Example: x = 1, 2, 3 gives y = 5, 8, 11. What is y when x = 4? y goes up by 3 each time. 11 + 3 = 14. Answer: 14
Linear Relations in Texas
In the Texas Essential Knowledge and Skills (TEKS), this is unit 17 of 22 in 7th grade Math, after Mean, Median & Mode and before Two-Step Equations.
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: Texas Education Agency (TEA)
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
What is the value of 7n − 3 when n = 3?
7n − 3
answer box
18
Hint: Replace n with 3: 7 × 3 − 3 = 21 − 3 = 18.
Question 2
A phone plan costs $27 a month plus $8 for each gigabyte of data. What is the bill, in dollars, for a month with 10 GB?
answer box
107
Hint: Start amount + rate × number: 27 + 8 × 10 = 27 + 80 = 107.
Question 3
Which point is on the graph of y = x − 4?
y = x − 4
- (-3, -7)
- (-2, -7)
- (3, -7)
- (-3, -8)
(-3, -7)
Hint: Substitute each x into the rule and see if you get the y. For x = -3: y = 1 × (-3) − 4 = -7, so (-3, -7) is on the line.
Question 4
This pattern keeps growing the same way. How many chairs are in Figure 19?
Figure 1: 6 chairs
Figure 2: 10 chairs
Figure 3: 14 chairs
Figure 4: 18 chairs
answer box
78
Hint: Each figure adds 4 chairs, so the rule is 4n + 2 for figure n. Figure 19: 4 × 19 + 2 = 78.
Question 5
Which equation matches the points on the graph?
- y = 3x − 1
- y = 4x + 1
- y = 3x + 2
- y = 3x + 1
y = 3x + 1
Hint: At x = 0 the point is at y = 1. Each step right, y goes up 3. So y = 3x + 1. Check another point: x = 1 gives y = 4.
Question 6
Which expression gives the value for any term number n?
n 1 2 3 4 value 2 6 10 14 - 4n
- 4n − 2
- 4n − 1
- 4n + 2
4n − 2
Hint: The value changes by 4 each time n goes up by 1, so the rule starts with 4n. At n = 1, 4n is 4 but the table shows 2, so subtract 2: 4n − 2.