Introduction to Linear Functions

Show your work for each problem.

1.
Which of the following is a linear function?
1. a)
2. b)
3. c)
4. d)
Answer:
is linear because it fits the form where and . The others have exponents, roots, or in the denominator.
2.
What is the slope of the function ?
Answer: 4
In the form , the slope is . Here, because is the number multiplying .
3.
What is the y-intercept of ?
Answer: 8
In , the y-intercept is . Here, . This is where the line crosses the y-axis.
4.
Which function has a slope of zero?
1. a)
2. b)
3. c)
4. d)
Answer:
can be written as , where . This is a horizontal line at .
5.
Find the value of when for the function .
Answer: 10
1. Write the original function y = 2x + 4
2. Substitute into the function. What is ? 6
3. Now add 4 to get the final answer. What is ? 10
6.
A phone plan costs 15 euros per month plus 2 euros per gigabyte of data. Which function represents the monthly cost?
1. a)
2. b)
3. c)
4. d)
Answer:
The slope is 2 (cost per GB) and the y-intercept is 15 (fixed fee). So where is gigabytes.
7.
Create a table of values for using . What is the constant rate of change?
Answer: 3
1. Calculate when : -1
2. Calculate when : 2
3. Calculate when : 5
4. What is the change in each time increases by 1? 3
8.
If a cyclist travels at 20 km/h, how far will they travel in 4 hours? Use .
Answer: 80
km. This is a linear function where speed is the slope.
9.
Which equation represents a line that goes DOWN from left to right?
1. a)
2. b)
3. c)
4. d)
Answer:
has a negative slope (), so the line goes down from left to right.
10.
A taxi charges 4 euros plus 1.50 euros per kilometer. Write the function and find the cost for an 8 km ride.
Answer: 16
1. What is the fixed cost (y-intercept)? 4
2. What is the cost per kilometer (slope)? 1.5
3. Write the function in the form y = 1.5x + 4
4. Calculate the cost for 8 km: 16
11.
Determine whether this table represents a linear function:
Answer: yes
1. What is the change in from to ? 3
2. What is the change in from to ? 3
3. What is the change in from to ? 3
4. Is the rate of change constant? (yes/no) yes
12.
Find the slope of the function if the points and are on the line.
Answer: 3
Slope = . The line rises 9 units for every 3 units to the right.
13.
Which statement is TRUE about the function ?
1. a)The slope is
2. b)The line rises from left to right
3. c)The y-intercept is
4. d)The line falls from left to right
Answer: The line falls from left to right
The slope is (negative), so the line falls from left to right. The y-intercept is , not .
14.
Write the equation of the line that passes through with slope .
Answer: y = 2x - 3
1. What is the slope ? 2
2. The point is on the y-axis. What is the y-intercept ? -3
3. Write the equation in the form y = 2x - 3
15.
What type of line does represent?
1. a)A diagonal line going up
2. b)A diagonal line going down
3. c)A horizontal line
4. d)A vertical line
Answer: A horizontal line
means every point has a y-coordinate of 4, regardless of x. This creates a horizontal line at height 4.
16.
For the function , what value of makes ?
Answer: 3
leads to , so . The point is where the line crosses the x-axis.