Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 7.2 Answer Key Writing and Graphing Equations in the Form y = mx + b.

## Texas Go Math Grade 7 Lesson 7.2 Answer Key Writing and Graphing Equations in the Form y = mx + b

**Texas Go Math Grade 7 Lesson 7.2 Explore Activity Answer Key**

Graphing Linear Relationships

Teresa signs up for a membership to rent video games. The company charges $5 per month and $2 per video game. Graph a linear relationship between the number of games Teresa rents and her monthly cost.

STEP 1: Make a table. Record different values for the linear relationship.

STEP 2: Use the table to create ordered pairs:

(0, 5), (1, 7), (2, 9), (3, 11), (4, 13)

Plot each ordered pair on the coordinate grid.

**Reflect**

Question 1.

Do the values between the points make sense in this context? Explain.

Answer:

This makes sense because the graphics show that when the number of lending increases, the price is rising.

**Your Turn**

**Write an equation to describe the linear relationship.**

Question 2.

The temperature of a pot of water is 45°F. The temperature increases by 20°F per minute when being heated.

Answer:

y = 20 ∙ x + 45

Question 3.

A bamboo reed is planted when it is 12 centimeters tall. It grows 2.2 centimeters per week.

Answer:

y = 22 ∙ x + 12

**Example 2**

Charlie starts with $350 in his savings account. He withdraws $15 per week from his account. Represent the relationship using a table, an equation, and a graph.

STEP 1: Make a table. Record different values for the linear relationship.

STEP 2: Write an equation for the amount of money y in the savings after x weeks. $350 minus $15 times the number of weeks

y = 350 – 15x

STEP 3: Use the table to create ordered pairs and then plot the data.

**Reflect**

Question 4.

Does it make sense to connect the points on the graph with a line? Explain.

Answer:

It makes sense, because in this way it is easier to see that when withdrawing money, the saved amount is reduced.

Question 5.

Does an ordered pair with a negative y-value make sense in the situation?

Answer:

It makes no sense to take negative values for y because it would mean that he takes more money than what he has on the account, which is impossible.

**Your Turn**

Question 6.

A bicycle rental company charges $18 to rent a bicycle, plus $7 for every two hours of rental time. Represent the relationship using a table, an equation, and a graph.

Answer:

Equation: 18 + 7 ∙ x = y

**Texas Go Math Grade 7 Lesson 7.2 Guided Practice Answer Key**

**Graph the linear relationship. (Explore Activity)**

Question 1.

A pool contains 5 liters of water, and 10 liters of water are being poured into the pool every 5 minutes.

Answer:

y = 2 ∙ x + 5

Ploted pairs on the coordinate grid are:

A = (0, 5)

More precisely in equation replace x with 0, and y with 5 for point A;

B = (10, 25)

Replace in equation x with 10, and y with 25 for point B.

**Write an equation to describe the linear relationships. (Example 1)**

Question 2.

A moving company charges a $50 flat fee and $55 per hour to move.

y = _______ x + _______

Answer:

y = 55 ∙ x + 50

Question 3.

Anne has $250 in a savings account. She withdraws $5 per month.

y = _______ x + _______

Answer:

y = -5 ∙ x + 250

Question 4.

Erin owns $375 worth of comic books. She spends $15 every week on new comic books. Represent the relationship using a table and an equation. (Example 2)

y = _______x + _______

Answer:

y = 15 ∙ x + 375

**Essential Question Check-In**

Question 5.

How can you use a table of data to write and graph a linear relationship?

Answer:

All the initial values that we get actually represent x, while all the values obtained based on the initial conditions by solving the equation represent y.

**Texas Go Math Grade 7 Lesson 7.2 Independent Practice Answer Key**

**A cab company charges a $3.50 boarding fee and $0.50 per mile.**

Question 6.

Write an equation to describe the relationship between the cost of the cab ride and the number of miles traveled.

Answer:

y = 0.5 ∙ x + 3.5

Question 7.

Graph the linear relationship.

Answer:

y = 0.5 ∙ x + 3.5

Question 8.

Draw Conclusions Does it make sense to draw a line through the points? Explain.

Answer:

It makes sense because in this way we easily notice how the billing increases in the miles ahead.

Question 9.

What If? Suppose that the boarding fee was changed to $5. How would the graph change?

Answer:

y1 = 0.5 ∙ x + 3.5

y2 = 0.5 ∙ x + 5

The value of the variable y1 has increased

(with that increase we got a variable y_2)

so the points on the graph are above the points before increasing the variable y1.

**For 10-13 write an equation to represent the given linear relationship. Then state the meaning of the given ordered pair.**

Question 10.

A plain medium pizza costs $8.00. Additional toppings cost $0.85 each. (4, 11.4)

Answer:

y = 0.85 ∙ x + 8

For x = 4 in the equation we get y = 11.4

Question 11.

Luis joined a gym that charges a membership fee of $99.95 plus $7.95 per month. (9, 171.5)

Answer:

y = 7.95 ∙ x + 99.95

For x = 9 in the equation we get y = 171.5

Question 12.

A tank currently holds 35 liters of water, and water is pouring into the tank at 15 liters per minute. (5.5, 117.5)

Answer:

y = 15 ∙ x + 35

For x = 5.5 in the equation we get y = 117.5

Question 13.

Jonas is riding his bicycle at 18 kilometers per hour, and he has already ridden for 40 kilometers. (6, 148)

Answer:

y = 18 ∙ x 40

For x = 6 in the equation we get y = 148

Question 14.

**Analyze Relationships** How can you use an equation of a linear relationship to verify the points on the graph of the relationship?

Answer:

Let the point A= (p, q) from the graph. By replacing the value in the equation y = mx + b, where x = p, y = q, if the left and right sides are equal, we have confirmed the relation between the equation and the graph.

Question 15.

**Multiple Representations** A furniture salesperson earns $750 per week plus a 15% commission on all sales made during the week.

a. Complete the table of data.

Answer:

b. Graph the values in the table.

Answer:

c. Write a linear equation to describe the relationship.

Answer:

y = 0.15 ∙ x + 750

Question 16.

Make a Conjecture Can you draw a straight line through the points? Explain.

Answer:

We can for the reason that all points are solutions of the same equation.

**H.O.T. Focus on Higher Order Thinking**

Question 17.

**Analyze Relationships** What are the advantages of portraying a linear relationship as a table, graph, or equation?

Answer:

The advantage of graphics, tables and equations is that it helps us to see the changes and understand them in easy way.

Question 18.

**Critical Thinking** Describe when it would be more useful to represent a linear relationship with an equation than with a graph.

Answer:

It would be more useful to present it through the equation because from the equation for the given value we can easily get points on the graph.

Question 19.

**Communicate Mathematical Ideas** How can you determine when to draw a line through the points on the graph of a linear relationship?

Answer:

Linear relationship can represent with equation. If all the points on graph are the solutions of the equation, then we can draw a line through them.