Texas Go Math Grade 6 Module 14 Answer Key Relationships in Two Variables

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Texas Go Math Grade 6 Module 14 Answer Key Relationships in Two Variables

Essential Question
How can you use relationships in two variables to solve real-world problems?

Texas Go Math Grade 6 Module 14 Are You Ready? Answer Key

Complete these exercises to review skills you will need for this chapter.

Multiply.

Question 1.
7 × 6 ____
Answer:
Solution to this example is given below
7 × 6 =? Use a related fact you know.
6 × 6 = 36.
Think:7 × 6 = (6 × 6) + 6
= 36 + 6
= 42
Final solution
42

Question 2.
10 × 9 ____
Answer:
Solution to this example is given below
10 × 9 = 7 Use a related fact you know.
9 × 9 = 81.
Think: 10 × 9 = (9 × 9) + 9
= 81 + 9
= 90
Final solution
90

Question 3.
13 × 12 ____
Answer:
Solution to this example is given below
13 × 12 =? Use a related fact you know.
12 × 12 = 144.
Think: 13 × 12 = (12 × 12) + 12
= 144 + 12
= 156
Final solution
156

Question 4.
8 × 9 ____
Answer:
Solution to this example is given below
8 × 9 =? Use a related fact you know.
8 × 8 = 64.
Think: 8 × 9 = (8 × 8) + 8
= 64 + 8
= 72
Final solution
72

Write the rule for each table.

Question 5.

Answer:
Compare the x- and y-values to find a pattern.
Each x-value is 7 times the corresponding y-value
Use the pattern to write an equation expressing y in terms of x
y = 7x
y = 7x Final solution
y = 7x

Question 6.

Answer:
Compare the x- and y-values to find a pattern.
Each x-value is 6 more than the corresponding y-value
Use the pattern to write an equation expressing y in terms of x
y = x + 6
y = x + 6 Final solution
y = x + 6

Question 7.

Answer:
For example let x₁ be 1 and x₂ be 3 and because of this y₁ will be -5 and y₂ will be -15. We will use equation of a line through those two points and get:
y – y₁ = \(\frac{y_{2} \cdot y_{1}}{x_{2}-x_{1}}\)(x – x₁)
y + 5 = \(\frac{-15+5}{3-1}\)(x – 1)
y + 5 = -5(x – 1)
y = -5x + 5 – 5
y = -5x
So,
required rute is y = -5x.
y = -5x

Question 8.

Answer:
Compare the x- and y-values to find a pattern.
Each x-value is 0.5 times the corresponding y-value
Use the pattern to write an equation expressing y in terms of x
y = 0.5x
y = 0.5x Final solution
y = 0.5x

Graph each point on the coordinate grid above.

Question 9.
B (0, 8)
Answer:
Solution to this example is given below
Start at the origin.
Move 0 units right
Then move 8 units up.
Graph point B( 0, 8).

Question 10.
C (2, 3)
Answer:
Solution to this example is gin below
Start at the origin
Move 2 units right
Then move 3 units up.
Graph point C( 2, 3).

Question 11.
D (6, 7)
Answer:
Solution to this example is given below
Start at the origin.
Move 6 units right
Then move 7 units up.
Graph point D( 6, 7).

Question 12.
E (5, 0)
Answer:
Solution to this example is given below
Start at the origin.
Move 5 units right
Then move 0 units up.
Graph point E( 5, 0).

Texas Go Math Grade 6 Module 14 Reading Start-Up Answer Key

Visualize Vocabulary
Use the ✓ words to complete the chart.

Understand Vocabulary

Complete the sentences using the preview words.

Question 1.
The numbers in an ordered pair are _____
Answer:
The numbers in an ordered pair are coordinates
We know that coordinates are ordered pairs formed of numbers so, the missing word is coordinates.

Question 2.
A ________________________ is formed by two number lines that intersect at right angles.
Answer:
A coordinate plane is formed by two number lines that intersect at right angles.

Coordinate plane is actually made of two number lines that intersect at right angles, so, missing word is coordinate plane.