Quiz about Linear Equation from Context

Question 1

The graph represents the height of a burning candle. What is the meaning of the y-intercept?

Accepted Answer

the original height of the candle

Answer

the time it takes to burn the entire candle

Answer

the rate at which the candle is losing height

Answer

the change in the height of the candle each hour

Question 2

Write a linear equation in slope-intercept form give the point and slope. (-6, -11); slope = 1/2

Accepted Answer

$$y=\frac{1}{2}x-8$$

Answer

$$y+6=\frac{1}{2}\left(x+6\right)$$

Answer

$$x-2y=16$$

Answer

$$y=\frac{1}{2}x-11$$

Question 3

Write a linear equation in point-slope form given the point and slope: (5, -9), slope = -2/5

Accepted Answer

$$y+9=-\frac{2}{5}\left(x-5\right)$$

Answer

$$y+5=-\frac{2}{5}\left(x-9\right)$$

Answer

$$y-5=-\frac{2}{5}\left(x+9\right)$$

Answer

$$y-9=-\frac{2}{5}\left(x+5\right)$$

Question 4

The aquarium is draining a large fish tank. The pump they are using can drain 24 gallons per hour. After 3 hours, there are 78 gallons left in the tank. Write an equation in slope-intercept form to model the water left in the tank, y, after x hours of draining. How many gallons were originally in the tank?

Accepted Answer

$$y=-24x+150$$ ; there was 150 gal in the tank initially

Answer

$$y=-24x+78$$ ; there was 78 gal in the tank initially

Answer

$$y=24x-150$$ ; there was 150 gal in the tank initially

Answer

$$y=150x-24$$ ; there was 24 gal in the tank initially

Question 5

Ben and Julia rented a truck from the same company to move to college. Ben drive 150 miles and paid $64.95 while Julia drove 84 miles and paid $45.15. What is the slope and what does it represent in context to the situation.

Accepted Answer

m = 0.30; it represents the cost per mile.

Answer

m = 0.30; it represents the initial fee for the moving truck

Answer

m = 19.95; it represents the initial fee for the moving truck

Answer

m = 3.33; it represents the cost per mile.

Question 6

Allie orders candles from an online company that offers flat rate shipping. She placed an order for 4 candles for $35. A few months later, she placed an order for 12 candles for $95. Write an equation in point-slope form to model the total cost, y, for ordering x candles. How much is shipping?

Accepted Answer

$$y-35=7.5\left(x-4\right)$$ ; shipping is $5

Answer

$$y+35=7.5\left(x+4\right)$$ ; shipping is $7.50

Answer

$$y-95=7.5\left(x-12\right)$$ ; shipping is $7.50

Answer

$$y+95=7.5\left(x+12\right)$$ ; shipping is $5

Question 7

Which equation represents the graph of the function with point (-2, 5) and slope of 3?

Accepted Answer

$$y-5=3\left(x+2\right)$$

Answer

$$y=3x+5$$

Answer

$$3x-y=11$$

Answer

$$y-5=3\left(x-2\right)$$

Question 8

What is the equation and slope of the line shown on the grid?

Accepted Answer

x = 6; slope is undefined

Answer

y = 6; slope is -1

Answer

x = 6; slope is zero

Answer

y = 6; slope is 6

Question 9

Write an equation in slope-intercept form given the point and slope: (-4, -7); slope = 1

Accepted Answer

$$y=x-3$$

Answer

$$y+7=x+4$$

Answer

$$y=x-7$$

Answer

$$x-y=3$$

Question 10

Anthony's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=57+6.3x, where y represents the expected quiz score and x represents hours spent on homework that week. What is the meaning of the x-value when y=99?

Accepted Answer

The number of hours a student should spend on their homework to expect a score of 99 on the quiz

Answer

A student's expected quiz score if they spend 1 hour on their homework

Answer

A student's expected quiz score if they spend 99 hours on their homework

Answer

How many hours a student spends studying all year

Question 11

At the beginning of spring, Lauren planted a small sunflower in her backyard. The sunflower's height in inches, h, after w weeks, is given by the equation h=9+3w. What could the number 9 represent in the equation?

Accepted Answer

The sunflower's height when it was planted

Answer

The sunflower's final height

Answer

The rate of change in the sunflower's height

Answer

The sunflower's height after one week

Question 12

Kylie is ordering a taxi from an online taxi service. She has to pay a flat charge just to order the taxi, and then has to pay per mile, depending on how far she travels. She wrote an equation to represent her total cost, y=3.5+2.3x, where y represents the total cost in dollars and cents, and x represents the number of miles she travels. What could the number 3.5 represent in the equation?

Accepted Answer

The flat charge to order the taxi

Answer

How much the taxi costs per mile

Answer

Total charge for one mile

Answer

How far Kylie can ride for $1

Question 13

Starting at noon, Emily observed the amount of snow on her lawn during a blizzard. She wrote an equation to represent s, how many inches of snow were on the lawn: s=0.024x+7, where x represents the number of minutes past noon. What could the number 0.024 represent in the equation?

Accepted Answer

How much more snow is added to the lawn every minute

Answer

The amount of snow on the lawn at 12:01 pm

Answer

The amount of snow on the lawn at noon

Answer

The total amount of snow

Question 14

Jocelyn is going to the amusement park, where she has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money Jocelyn will spend is given by the equation y=3.5x+28, where y represents the total amount of money, in dollars and cents, and x represents the number of rides Jocelyn goes on. What could the number 28 represent in the equation?

Accepted Answer

The cost to get into the amusement park

Answer

The total amount Jocelyn will spend if she goes on 1 ride

Answer

The change in total amount of money for each additional ride she goes on

Answer

The total amount Jocelyn will spend if she goes on 100 rides

Linear Equation from Context

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