Quiz about Linear Equations (Slope-intercept and Standard Form)

Question 1

What is the interpretation of the slope in the situation where the equation relating the diameter of a hole (mm) in a plastic cup and the amount of water (mL) in the cup 5 seconds after being filled is found to be y = -10.37x + 500?

Accepted Answer

For each increase of 1 mm in diameter of the hole, the cup loses 10.37 mL of water.

Answer

For every additional second, the cup loses 10.37x mL of water.

Answer

For each decrease of 1 mm in diameter of the hole, the cup loses 10.37 mL of water.

Answer

If the water is let go for 1 second less, 10.37 mL water is lost.

Question 2

What is the meaning of the slope of the equation C(x) = 385 + 0.45x in the context of the cost to make DVDs, where x is the number of DVDs?

Accepted Answer

It is the cost for printing each DVD.

Answer

It is the cost for printing 45 DVDs.

Answer

It is the flat rate for making each DVD.

Answer

It is the flat rate for making 385 DVDs.

Question 3

What is the meaning of the slope in the model p = 10 + 0.3t for Heather's typing?

Accepted Answer

It is the number of pages per minute Heather types.

Answer

It is the number of words Heather types after lunch.

Answer

It is the total number of pages Heather types for the report.

Answer

It is the number of minutes Heather needs to type a single page.

Question 4

What is the meaning of the slope in the equation g = 4.77s + 12.44, where s is the number of people in a household and g is the garbage produced per week in pounds?

Accepted Answer

For every person living in a household, the household generates 4.77 pounds of garbage per week.

Answer

Every pound of garbage produced per week represents 4.77 people per household.

Answer

Every pound of garbage produced per week represents 12.44 people per household.

Answer

For every person living in a household, the household generates 12.44 pounds of garbage per week.

Question 5

Which statement most accurately describes the slope of this data set?

Accepted Answer

The candle burns 3 inches every 4 hours.

Answer

The candle burns 3 inches every hour.

Answer

The candle burns 4 inches every hour.

Answer

The candle burns 4 inches every 3 hours.

Question 6

The value (V) of property in a particular area depends on the land and the square footage of the house according to the equation given in the box, where x represents the square footage of the house, in square feet. What is the meaning of the V-intercept and slope in the context of the equation V = 80x + 6,000?

Accepted Answer

The V-intercept is the value of the land without the house, and the slope is the rate of increase of the value of the house for each increase in square footage.

Answer

The V-intercept is the value of the house not including the land, and the slope is the total value of the house and land.

Answer

The V-intercept is the total value of the house and land, and the slope is the value of the house not including the land.

Answer

The V-intercept is the rate of increase of the value of the house for each increase in square footage, and the slope is the value of the land without the house.

Question 7

The equation P = 16,250 + 75n can be used to determine the population, P, of a city after, n, years. Which statement is true?

Accepted Answer

The initial population was 16,250 people.

Answer

The population after 10 years was 16,325 people.

Answer

The population increases by 16,250 people each year.

Answer

The population increases by 16,250 people every 75 years.

Question 8

The linear equation y = 400 + 50x represents the total cost, y, per hour, x, for the services of a lawyer at a law firm. The lawyer charges a flat retainer fee and then charges per hour of work done. What does the y-intercept of the equation represent in this context?

Accepted Answer

the flat retainer fee of $400

Answer

the cost of $50 per hour of work

Answer

the cost of $400 per hour of work

Answer

the flat retainer fee of $50

Question 9

A florist buys x dozen roses and y dozen carnations for a wedding. The roses cost $16 per dozen, and the carnations cost $9 per dozen. If the florist pays a total of $218, which equation represents the situation?

Accepted Answer

16x + 9y = 218

Answer

16x - 9y = 218

Answer

9x + 16y = 218

Answer

9x - 16y = 218

Question 10

An organic farmer raises wheat and corn on a 144-acre farm. After doing some market research, the farmer decides to plant 25% more corn than wheat. The price of corn is $8 per bushel, and the price of wheat is $5 per bushel. If the farmer earns $3,000 from selling x bushels of corn and y bushels of wheat, which equation represents the situation?

Accepted Answer

8x + 5y = 3,000

Answer

5x - 8y = 3,000

Answer

5x + 8y = 3,000

Answer

8x - 5y = 3,000

Question 11

A landscaping service prunes trees and trims shrubs for its customers. On average, it takes x minutes to prune each tree and y minutes to trim each shrub. If the landscaping service prunes 6 trees and trims 15 shrubs in a total of 180 minutes, which equation represents the situation?

Accepted Answer

6x + 15y = 180

Answer

15x + 6y = 180

Answer

15x - 6y = 180

Answer

6x - 15y = 180

Question 12

A restaurant has rectangular and circular tables. The rectangular tables, r, seat 8 people, and the circular tables, c, seat 10 people. Which equation represents the total number of people, p, who can be seated at the tables?

Accepted Answer

8r + 10c = p

Answer

18(c + r) = p

Answer

10r + 8c = p

Answer

c + r = 18p

Question 13

There are d dimes and q quarters in a jar. If the total worth of the dimes and quarters is $80, which equation represents the situation?

Accepted Answer

0.1d + 0.25q = 80

Answer

d + q = 80

Answer

10d + 25q = 80

Answer

0.01d + 0.25q = 80

Question 14

A family is traveling a total distance of 532 miles. If the family travels at an average speed of 57 miles per hour, which equation represents the number of miles remaining, m, after h hours?

Accepted Answer

m = 532 - 57h

Answer

m = 532 + 57h

Answer

m = 532h - 57

Answer

m = 532h + 57

Question 15

Which choice matches the equation of a line with a y-intercept of 6 and an x-intercept of 6?

Accepted Answer

y = -x + 6

Answer

y = -6x

Answer

6y = -6x

Answer

y = x - 6

Question 16

Which equation is written in slope-intercept form and has a slope of -5 and a y-intercept of 5?

Accepted Answer

y = -5x + 5

Answer

y = 5x - 5

Answer

y - 10 = -5(x + 1)

Answer

y + 5 = -5(x - 2)

Question 17

What is the standard form of the equation of the line with a slope of 10 and passing through (-2, 5)?

Accepted Answer

-10x + y = -52

Answer

10x - y = 52

Answer

-10x + y = 25

Answer

10x - y = -25

Question 18

The graph shows the relationship between the expected mileage for two new cars according to fuel economy stickers and the actual mileage drivers obtained. Based on the graph, select all functions that represent this relationship.

Accepted Answer

y = (6/7)x

Accepted Answer

7y = 6x

Answer

y = x

Answer

y = (6/7)x - 3

Answer

y = (6/7)x - 4

Question 19

Melanie and Denzel are buying strawberries to make a cobbler. The friends have $12 to spend, and strawberries cost $3.99 per pound. Which function represents the amount of money Melanie and Denzel have left, f(x), after buying x pounds of strawberries?

Accepted Answer

f(x) = 12 - 3.99x

Answer

f(x) = 12 + 3.99x

Answer

f(x) = 3.99x - 12

Answer

f(x) = 3.99x + 12

Question 20

A linear function has an initial value of 8 and decreases 6 y-units for every increase of 1 x-unit. Which equation represents the function?

Accepted Answer

f(x) = -6x + 8

Answer

f(x) = -1/6x + 8

Answer

f(x) = 8x - 6

Answer

f(x) = 8x - 1/6

Question 21

Which equation represents the line formed by drawing a line through the two points in this graph? A coordinate grid with two points marked, one at (-3, 2) and another at (0, 0).

Accepted Answer

y = -1/3x + 3/3

Answer

y = 5x + 15

Answer

y = -1/3x - 3

Answer

y = -x - 15

Question 22

Which of the following situations can be modeled by the equation below? 5x = 3x + 8

Accepted Answer

The cost of x sandwiches that cost $5 each equals the cost of x + 8 hot dogs that cost $3 each.

Answer

The cost of x sandwiches that cost $5 each equals the cost of 3x hot dogs that cost $8 each.

Answer

The cost of x sandwiches that cost $5 each is $8 less than the cost of x hot dogs that cost $3 each.

Answer

The cost of x sandwiches that cost $5 each is $8 more than the cost of x hot dogs that cost $3 each.

Question 23

Which of the following situations can be modeled by the equation below? 5w = 3w + 9

Accepted Answer

Five times the width of a rectangle is 9 inches more than 3 times the width.

Answer

Three times the width of a rectangle is 9 inches more than 5 times the width.

Answer

Five times the width of a rectangle equals 3 times the sum of the width and 9 inches.

Answer

Three times the width of a rectangle equals 5 times the sum of the width and 9 inches.

Question 24

Which of the following situations can be modeled by the equation below? 8x - 24 = 5x

Accepted Answer

The cost of x - 24 CDs at $8 each equals the cost of x CDs at $5 each.

Answer

The cost of x + 24 CDs at $8 each equals the cost of x CDs at $5 each.

Answer

The cost of x CDs at $8 each is $24 less than the cost of x CDs at $5 each.

Answer

The cost of x CDs at $8 each is $24 more than the cost of x CDs at $5 each.

Question 25

A teacher plans to buy air fresheners that cost $3.50 each. If the teacher can spend $10 on the air fresheners and has a $4 discount coupon, which equation represents the number of air fresheners, x, the teacher can buy?

Accepted Answer

3.50x - 4 = 10

Answer

3.50x + 4 = 10

Answer

4x + 3.50 = 10

Answer

4x - 3.50 = 10

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