Solved Examples and Worksheet for Meaning of Slope and Intercepts in Graphs and Situations

Q1Sam took a loan to purchase a vehicle. He paid back an intial amount of $230 and paid the the remaining amount in equal instalments. Which graph represents this situation?


A. Graph 1
B. Graph 3
C. Graph 4
D. Graph 2

Solutions
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Step: 1
Graph 1 shows the initial amount apid by Sam and the amount paid by him in subsequent months.
Step: 2
So, graph 1 is the right choice.
Correct Answer is :   Graph 1
Q2Brian rides a bike at the rate of 30mph. How will the graph function change if the bike is ridden slower?
A. The y-intercept will increase.
B. The y-intercept will decrease.
C. The slope will increase.
D. The slope will decrease.

Solutions
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Step: 1
Slope is used to find the rate of speed the bike.
Step: 2
If the speed of the bike decreases, then the value of slope decreases.
Step: 3
Hence, the slope will decrease if the bike is ridden slower.
Correct Answer is :   The slope will decrease.
Q3The graph compares the population of four different states in the year 2003. Each city has different initial population. Which state has the highest population growth?

A. City P
B. City S
C. City R
D. City Q

Solutions
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Step: 1
Rate of population growth can be found by using slope.
Step: 2
Among the graph, it is obvious that the graph of City P has highest slope.
Step: 3
So, City P has the highest population growth.
Correct Answer is :   City P
Q4A box has x cents and y quarters with a total value of $65. What does the y-intercept of the graph of 0.01x + 0.25y = 65 tells?
A. number of nickels and number of dimes is 65
B. number of cents if there are no quarters
C. number of quarters if there are no cents
D. there are 65 coins in the box

Solutions
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Step: 1
0.01x + 0.25y = 65
  [Original equation.]
Step: 2
To find y-intercept, let x = 0.
Step: 3
0.01(0) + 0.25y = 65 => y = 260
Step: 4
y = 260 represents the number of quarters if there are no cents.
Correct Answer is :   number of quarters if there are no cents
Q5The population of a state in millions from 1993 is modeled by the equation y = 1.25x + 1.6, where x denotes the number of years since 1993. Which of the following does the y-intercept represents?

A. population in the year 1993
B. change in population
C. population after one year
D. None of these

Solutions
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Step: 1
y = 1.25x + 1.6
  [Original equation.]
Step: 2
To find the y-intercept, let x = 0.
Step: 3
⇒ y = 1.25(0) + 1.6
⇒ y = 1.6
Step: 4
y = 1.6 represents the population in the year 1993.
Step: 5
So, the y-intercept represents the population in the year 1993.
Correct Answer is :   population in the year 1993
Q6A rental car company charges $65 to rent a car and an additional $0.25 per mile the car is driven. If y = $0.25x + $65 represents the total rent charged, what does the y-intercept represents?

A. initial rental charges $65.
B. number of miles the car travels
C. initial speed of the car
D. the rate of change in rent per mile

Solutions
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Step: 1
y = $0.25x + $65
  [Original equation.]
Step: 2
To find y-intercept, let x = 0.
Step: 3
y = $0.25(0) + $65 = $65
  [Substitute the value of x in the equation.]
Step: 4
⇒ y = $65
Step: 5
Therefore the initial rental charges of a car, y = $65 represents the y-intercept of the given equation.
Correct Answer is :   initial rental charges $65.
Q7Jim drives a car at the rate of 40mph. How will the graph function change if the car is driven slower?

A. The y-intercept will decrease.
B. The y-intercept will increase.
C. The slope will decrease.
D. The slope will increase.

Solutions
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Step: 1
Slope is used to find the rate of speed of the car.
Step: 2
If the speed of the car decreases, then the value of slope decreases.
Step: 3
Hence, the slope will decrease if the car is driven slower.
Correct Answer is :   The slope will decrease.
Q8The population of a state in millions from 2003 is modeled by the equation y = 2.75x + 3.8, where x denotes the number of years since 2003. Which of the following does the y-intercept represents?
A. rate of change in population
B. number of years
C. population after 10 years
D. population in the year 2003

Solutions
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Step: 1
y = 2.75x + 3.8
  [Original equation.]
Step: 2
To find the y-intercept, let x = 0.
Step: 3
⇒ y = 2.75(0) + 3.8
  [Substitute the value of x in the equation.]
Step: 4
⇒ y = 3.8
Step: 5
= 3.8 represents the population in the year 2003.
Step: 6
So, the y-intercept represents the population in the year 2003.
Correct Answer is :   population in the year 2003
Q9The graph shows the relationship between rental charges of a car and the number of hours the car travelled. Interpret the meaning of the slope as a rate of change.

A. Rental charges for every hour decreases by $10.
B. Rental charges for every additional hour increases by $8.
C. Rental charges for every additional hour increases by $10.
D. Rental charges for every hour decreases by $8.

Solutions
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Step: 1
The graph indicates that, the initial rent of a car is $10 and charges for every additional hour increases by $8.
Step: 2
we can interpret the slope as a rate of change in rental charges for every hour.
Step: 3
So, the graph best suits the statement 'Rental charges for every additional hour increases by $8.'
Correct Answer is :   Rental charges for every additional hour increases by $8.

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