IM Lesson 3-6 Grade 8

IM Lesson 3-6 Grade 8

More Linear Relationships

Proportional Relationships

Proportional Relationships

Pass through the point (0,0).

Form a straight line on a graph.

Have a constant of proportionality (slope).

Equation: y=mx

Linear Relationships

Form a straight line on a graph.

Have a constant rate of change (slope).

Equation: y=mx+b

Multiple Select

Which of the following are proportional?

• y= 5x

• c= 2/3m

• h= 3v + 3

• k = 194

Multiple Select

Which of the following are non-proportional linear relationships?

• y= 3x + 7

• t=14

• k= 2q +4

• 7= 2y

Multiple Choice

Which graph represents a proportional relationship?

Multiple Choice

What does the slope mean in the following situation?

Lin’s dad bought a tablet. He pays the same amount each month for a subscription to a movie streaming service. The graph represents how much money he spent, y, for the tablet and x months of the service.

• The tablet cost $10 to purchase.

• The tablet costs $10 per month to use.

Multiple Choice

What does the y-intercept  mean in the following situation?

Lin’s dad bought a tablet. He pays the same amount each month for a subscription to a movie streaming service. The graph represents how much money he spent, y, for the tablet and x months of the service.

• The tablet cost $40 to purchase.

• The tablet costs $40 per month to use.

Multiple Choice

What does the slope represent in the following?

Diego puts his piggy bank on his desk. Each week he adds the same amount of money to his bank. The graph represents the amount in the piggy bank, y, after x weeks. The slope of the line is 5.

• Diego starts with $5 in his bank.

• Diego adds $5 per week to his bank.

Multiple Choice

What does the y-intercept represent in the following?

Diego puts his piggy bank on his desk. Each week he adds the same amount of money to his bank. The graph represents the amount in the piggy bank, y, after x weeks.

• Diego starts with $10 in his bank.

• Diego adds $10 per week to his bank.

Open Ended

What does the slope mean in the following?

Lin’s mom pays the same amount each month for internet service for her business tablet. The graph represents how much money she spent, y, for x months of service.

Open Ended

What does the y-intercept mean in the following?

Lin’s mom pays the same amount each month for internet service for her business tablet. The graph represents how much money she spent, y, for x months of service.

Vertical or Y-Intercept

The vertical or y-intercept is where the line crosses the y-axis. This is the starting point in a situation. For example, in the graph the vertical intercept is (0,1). Which means that at zero days the plant was already 1cm tall.

Summary

At the start of summer break, Jada and Lin decide to save some of the money they earn helping out their neighbors to use during the school year. Jada starts by putting $20 into a savings jar in her room and plans to save $10 a week. Lin starts by putting $10 into a savings jar in her room plans to save $20 a week. Here are graphs of how much money they will save after 10 weeks if they each follow their plans:

Summary

The value where a line intersects the vertical axis is called the vertical intercept. When the vertical axis is labeled with a variable like y

this value is also often called the y-intercept. Jada's graph has a vertical intercept of $20 while Lin's graph has a vertical intercept of $10. These values reflect the amount of money they each started with. At 1 week they will have saved the same amount, $30. But after week 1, Lin is saving more money per week (so she has a larger rate of change), so she will end up saving more money over the summer if they each follow their plans.

Open Ended

Explain what the slope means in this situation:

The amount of money, y, in a cash box after x tickets are purchased for carnival games. The slope of the line is 0.25 and the y-intercept is 8.

Open Ended

Explain what the y-intercept means in this situation:

The amount of money, y, in a cash box after x tickets are purchased for carnival games. The slope of the line is 0.25 and the y-intercept is 8.

Open Ended

Explain what the slope means in this situation:

The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.

Open Ended

Explain what the y-intercept means in this situation:

The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.

Multiple Choice

Customers at the gym pay a membership fee to join and then a fee for each class they attend. Here is a graph that represents the situation.

What does the slope of the line shown by the points mean in this situation?

• Every class costs $20

• Each class costs $60

Multiple Choice

Customers at the gym pay a membership fee to join and then a fee for each class they attend. Here is a graph that represents the situation.

What does the y-intercept of the line shown by the points mean in this situation?

• Gym Membership costs $20

• Gym Membership costs $60