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Mathematics
8th
grade
3-4: Construct Functions to Model Linear Relationships
20 questions
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- 1. Multiple Choice
How can you write the equation for a linear function if you know only two ordered pairs for the function?
Use the two ordered pairs to find the slope (m). Then substitute the slope and one set of ordered pairs into y=mx+b to solve for b.
Use the two ordered pairs to find the y-intercept (b). Then substitute the y-intercept and one set of ordered pairs into y=mx+b to solve for m.
Use the two ordered pairs to find the value of y. Then substitute the the value of y and one set of ordered pairs into y=mx+b to solve for x.
Use the two ordered pairs to find the value of x. Then substitute the the value of x and one set of ordered pairs into y=mx+b to solve for y.
- 2. Multiple Choice
A line passes through the points (5, –7.5) and has a y-intercept 10.
Which is a linear function in the form of y = mx + b for this line?
y = 0.5x + 10
y = –1.5x + 10
y = –3.5x + 10
y = 10x – 3.5
- 3. Multiple Choice
Write a function in the form y=mx+b for the line that passes through the points (2,4) and (6,16)
y = 3x - 2
y = 2x + 4
y = 6x + 16
y = 2x + 6
- 4. Multiple Choice
Max puts a stopper in the bathtub and turns on the faucet at t = 0.
After 5 minutes, there are 11 gallons of water in the tub and after 10 minutes, there are 22 gallons in the tub.
Write an equation that relates the number of gallons, g, to the time, t.
Does the relationship represent a linear function? Justify your response.
g = 2.2t; The equation represents a linear function because the equation is in the form y = mx.
g = 2.2t; The equation does not represent a linear function because the equation is not in the form y = mx + b.
g = 4.4t; The equation represents a linear function because the equation is in the form y = mx.
g = 4.4t; The equation does not represent a linear function because the equation is not in the form y = mx + b.
- 5. Multiple Choice
Sierra is building a skateboard ramp.
She wants the ramp to have a height, h, of 15 inches and a base length, l, of 54 inches.
Which linear function models the situation?
y = (5/18)x
y = (18/5)x
y = 5x + 18
y = 18x + 5
- 6. Multiple ChoiceWhat is the equation for this line?y = x - 2y = x + 2y = 2xy = -x + 2
- 7. Multiple ChoiceFind the slope given the following points: (5,1) and (3,1)m=1/4m=0m=1m=undefined
- 8. Multiple ChoiceLee charges $3 for a basket and $2.50 for each pound of fruit picked at the orchard. Write an equation in y = mx + b form for the total cost of x pounds of fruit from the orchard.y = 3x + 2.5y = 2.50x + 3y = 2.50xy = 3x + 2.50
- 9. Multiple ChoiceWhich equation matches the table?y = x + 5y = 5xy = x - 5x = y - 5
- 10. Multiple ChoiceBowling costs $4 for shoe rental plus $5 for every game. Which equation shows how much it costs to go bowling for x games?y = 4 + 5xy = 5 + 4xy = 4•5•xy = 5x - 4
- 11. Multiple ChoiceWhat is the slope?1/2273
- 12. Multiple Choice
The deli charges $7.50 for a salad weighing 3 pounds. A salad weighing 4 pounds costs $9.00. What equation can be used to represent the cost of the salad (y) , for the (x) pounds of salad?
y = 1.5x + 3
y = -1.5x + 3
y = 1.5x - 3
y = -1.5x - 3
- 13. Multiple ChoiceWhich situation could match the depicted graph?The rate of change is a loss of one gallon each hourThe rate of change is an increase in temperature related to timeThe rate of change describes gas mileage related to engine sizeThe rate of change is a constant 25 miles per hour
- 14. Multiple Choice
What is another name for the rate of change?
slope
y-intercept
independent variable
dependent variable
- 15. Multiple Choice
What is another name for the initial value?
slope
y-intercept
independent variable
dependent variable
- 16. Multiple Choice
How would you write the equation with a rate of change of 2/3 and an initial value of -3
y=3/2x+3
y=2/3-3
y=2/3x-3
I don't have a clue
- 17. Multiple Choice
The distance in miles, y, a rower in a canoe is from the dock after rowing x hours is represented by the equation y = 5x + 11. What does the y-intercept represent in this situation?
The speed of the current
The speed of the rower/canoe
The distance the rower is from the dock when he began rowing.
The average speed of the oar as it passes through the water
- 18. Multiple Choice
Debbie is a server at a new restaurant which is trying a new way to pay their servers. Debbie's total earnings for each day can be represented by the equation y=0.10x +50, where x is Debbie's total food sales for the day. What is represented by the slope in this equation?
Debbie's set commission on her food sales paid for by the restaurant.
Debbie's set salary for the day.
Debbie's portion of beverage sales.
Debbie's free food she gets to eat.
- 19. Multiple ChoiceIs the following equation proportional or non proportional:
y= 4xProportionalNon Proportional - 20. Multiple ChoiceIs the following equation proportional or non proportional:
y= 4x - 5ProportionalNon Proportional - Answer choicesTagsAnswer choicesTags