8.SP.3 Part 2

8.SP.3 Part 2

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Linear Equation formula > y=mx + b

• m in the formula is the slope or rate of change

• b in the formula is the y-intercept or the initial value

Example 1 : Lets dissect y=3x + 10

• What is the slope?

• 3

• What is the initial value?

• 10

• What is the y-intercept?

• 10

Multiple Choice

What is the rate of change of the following equation: y=4x + 3

• 3

• 4

• x

Multiple Choice

What is the initial value of the following equation: y= 3 + 4x

• 3

• 4

• x

Tackling this Standard 8.SP.3

• This standard is mostly word problems

• Look for keywords that could mean initial value (started with, had, before, per trip, etc.)

• Look for keywords that could mean slope or rate of change (each day, each hour, etc.)

Example 2: A taxi company charges $10 per trip + $0.75 for every mile traveled. The total charge for taking a taxi can be modeled by the linear equation . 

• What is the slope or rate of change?

• $0.75

• What is the initial value (look for each or per)?

• $10

Multiple Choice

Quincy went to the movie theater. He bought a ticket for the movie and some snacks. The function below represents the cost of one movie ticket and some number of snacks (s). c = 2.5s + 9

What does the y-intercept of the question represent?

• Cost of snacks

• Total cost of movie and snacks

• Number of snacks purchased

• Cost of one move ticket

Multiple Choice

Of the equations listed below, which has the greatest initial value?

• y = 6 + 3x

• y = -x + 10

• y = 4 + 2x

Multiple Choice

Of the equations listed below, which has the lowest value for a y-intercept?

• y = 6 + 3x

• y = -x + 10

• y = 4 + 2x

Multiple Choice

Of the equations listed below, which has the steepest slope? (if graphed the line would be closer to the y-axis than the x-axis)

• y = 6 + 3x

• y = -x + 10

• y = 4 + 2x

Plug in values

• If you are given a question that is asking for a number as a response, plug in answer choices into the equation and test for the correct answer.

• y=5x + 10, what value of x will make my y value equal to 25? 1, 2, or 3?

• 15=5(1) + 10

• 20=5(2) + 10

• 25=5(3) + 10

Multiple Choice

Quincy went to the movie theater. He bought a ticket for the movie and some snacks. The function below represents the cost of one movie ticket and some number of snacks (s). c = 2.5s + 9

The total cost will be $26.50 after how many snacks have been purchased?

• 5

• 6

• 7

• 8

Multiple Choice

A science class collected data measuring the amount of water in a bucket that was out in the Sun. The equation w= -1.5h + 18 represents how much water, w , was in the bucket after hours, h. According to this equation, how many hours did take for the bucket to be emptied?

• 6

• 10

• 12

• 18

Multiple Choice

The equation t=2/3p + 12 is a function describing the wait time, t , in minutes, for a person to get onto a certain ride at a theme park on a Saturday afternoon. The number of people ahead in line is represented by p. If 27 people are ahead of Brandon in line, how long, in minutes, will he expect to wait?

• 8

• 12

• 27

• 30

Multiple Select

Wesley is studying the growth of tomato plants for a science project. He plants tomato plant and measures its height every week. The function shown below represents the height of the plant, h, in inches, after w weeks. h = 3w + 5 Which of the following observations made from the results are true? Select all that apply.

• The initial height of the plant was 5 inches.

• After 5 weeks, the plant will be 20 inches tall.

• The height of the plant will increase 5 inches every week.

• The initial height of the plant was 3 inches.

• The height of the plant will increase 3 inches every week.