Comparing Ratios of Tables, Graphs and Situations

Multiple Choice

BELL-RINGER QUESTION #1

What would be the image of C using the rule (x, y) → (x + 8, y - 4), if vertex C is at (4, -3)?

• C(12, -7)

• C(-4, 1)

• C(-8, 4)

• C(4, 7)

Graphing

BELL-RINGER QUESTION #2

Triangle KLM has vertices:

K(−1, 2), L(2, 3), and M(−3, 6).

A translation rule of (x, y) → (x - 1, y - 4) maps triangle KLM to triangle K′L′M′ making the image K′(−2, −2).

Plot the coordinates of vertices L′ and M′.

Dropdown

Choose the correct equation to match the description. Then discuss to compare the equations. REFER BACK TO THE NOTES OF RATIOS



1. The number of in-state students enrolled, y, for x total number of students enrolled.​ ​

Select answer

​

2. The number of out-of-state students enrolled, y, for x total number of students enrolled.​ ​

Select answer

​

3. The number of in-state students enrolled, y, for x out-of-state students enrolled.​​ ​

Select answer

4. The number of out-of-state students enrolled, y, for x in-state students enrolled.​​ ​

Select answer

Graphing

Create a graph that displays the ratio of the given statement.

5. "The number of in-state students enrolled, y, for x total number of students enrolled."

Equation: y=3/5x

Graphing

Create a graph that displays the ratio of the given statement.

6. "The number of out-of-state students enrolled, y, for x total number of students enrolled."

Equation: y=2/5x

Graphing

Create a graph that displays the ratio of the given statement.

7. "The number of in-state students enrolled, y, for x out-of-state students enrolled."

Equation: y= 3/2x

Graphing

Create a graph that displays the ratio of the given statement.

8. "The number of out-of-state students enrolled, y, for x in-state students enrolled."

Equation: y= 2/3x

Multiple Choice

9. Determine which line represents each relationship.

"The number of in-state students enrolled in a university."

HINT: Find a point on the graph that has the same ratio as 3:5

• Graph of line y1

• Graph of line y2

Multiple Choice

10. Determine which line represents each relationship.

"The number of out-of-state students enrolled in a university."

HINT: Find a point on the graph that has the same ratio as 2:5

• Graph of line y1

• Graph of line y2

Graphing

11. The ratio of the number of students who enjoy music to the total number of students is 20:25, which is slightly more than the ratio of in-state students enrolled. Use the given graph to display this ratio.

HINT: Simplify the ratio

Graphing

12. The ratio of students who work full-time to the total number of students is 5:25, which is less than the ratio for out-of-state enrolled students at the university. Use the given graph to display this ratio.

HINT: Simplify the ratio

Steepness of a line refers to slope, that is how quickly a line rises or falls as you move across a graph.

What is "steepness"?

​Video Notes
Steepness of Linear Graphs

Directions: From the video provided, take notes in your math journals.

Multiple Select

Daysia attends college in another state. During summer break, she drives home from college to visit her family and friends.

13. What is the ratio/constant of proportionality for distance (y) to time (x). Select all answers that apply

HINT: Simplify the ratio

• 60 miles per hour

• 60:1

• 60/1

• 1:60

Open Ended

One of Daysia’s high school classmates, Tyler, attends the same college.  He also drives home during the summer break but takes a different route.

14. Analyze the graph displayed and use DESMOS to compare with Daysia's proportional relationship. Who drives faster-Daysia or Tyler? Write your reasoning and explain in detail.

Open Ended

15. What is the meaning of the constant of proportionality from the given equation?

Reorder

16. Rank the friends in order from the shortest distance (less steep) traveled to the longest distance (more steep).

• Tyler

• Alisha

• Daysia

1

2

3

• 1
• 2
• 3

Multiple Choice

Check for Understanding

17. A full box of rice contains 10 servings. Which graph shows the proportional relationship between the number of boxes of rice and the total number of servings?

Multiple Choice

Exit Ticket 10/16

From the equation y=20x, where x represents the number of boxes and y is the total number of pencils, which statement best describes the relationship of the equation?

• The equation represents a relationship which is non-linear.

• The equation represents a relationship which is linear but not proportional.

• The equation represents a relationship which is linear and proportional.

• None of the above