Vocabulary
Writing Linear Functions
Graphing Linear Functions
Slope
Linear Functions Word Problems
Miscellaneous
100
A mapping, or, pairing, of input values with output values.
A relation
100
Write a linear function with a slope of -9 and a y-intercept of 5
y =-9x+5
100
Does the table represent a linear or nonlinear function? Explain using the phrase "constant rate of change."
x y
2 9
4 18
6 27
8 36
This represents a linear equation because x and y have a constant rate of change. Every x has one and only one y.
100
Identify the slope of the linear equation
y = -x + 6
The slope is -1
100
What are the two forms we have learned that can produce a linear function?
Slope Intercept form
Standard form
100
Function or not?
(-2,3), (-1,3), (8,4), (11,2)
yes
200
The set of all input values, independent variable, x-values.
Domain
200
Write a linear function in standard form where A=2 B=-4 and C=19
2x-4y=19
200
In the graph of x = 4, does this represent a linear or nonlinear function? Explain using the terms function, inputs and outputs.
This graph would represent neither linear or nonlinear because a vertical line is not considered a function as the input 4 is paired with multiple outputs.
200
What is the slope of a horizontal line?
The slope is 0.
200
Your friend runs at a pace of about 5 miles per hour. The table represents the number of hours (x) and the number of miles (y). Is the domain discrete or continuous? Explain.
x y
0 0
1 5
2 10
3 15
The domain is continuous; a person can run for part of an hour.
200
Solve the equation for x:
2(x + 3) = 14
x = 4
300
The definition of slope is...
A nonvertical line, that represents the ratio of the vertical change to the horizontal change. Denoted as "m".
300
Write the linear function in this graph:
y=20x-15
300
DAILY DOUBLE!!!!
The given table shows a linear function.
What is the missing number in the table?
x 0 2 4 6
y -1 1 ? 5
3
300
Is the function represented by the ordered pairs linear or nonlinear? Explain.
(0,2) (3,14) (5,22) (9,38) (11,46)
This represents a linear function. Both x and y increase by a constant rate of change.
300
Clarence wanted to see how high his football would fly up into the air. The graph represents the path from his hands and back down when he caught the ball. Approximate where the function is positive and negative.
Positive at 1<x<5
Negative at x<1 and x>5
300
Describe the graph and slope of y=5
horizontal , m= 0
400
The set of all output values, dependent variable, y-values.
Range.
400
Write a linear function that passes through the points (0,2) and (-4,5).
y= 3/4x +2
400
Would the equation below produce a linear or nonlinear function? Explain using the phrase "slope-intercept form," and give the equation in slope-intercept form.
18x - 2y = 26
The equation would produce a linear function. It can be put into slope intercept form as y = 9x - 13.
400
Find the slope of a linear function that contains the points (-2 , 8) and (5 , -13)
-3
400
Let F(x) be the yearly life insurance rate for people whose age is x years old above the age of 60.
1. F(73)=3x+2050
2. F(84)=40x-1000
3. F(66)=-70+2x+2100
1. $2,269
2. $2,360
3. $2,162
400
Identify the slope and y-intercept of the standard form equation
-5x + 3y = -15
Slope intercept form y = (5/3)x - 5
Slope: 5/3
y-intercept: -5
500
Define a function.
A relation for which each input has exactly one output. For each x there is one and only one y.
500
Write x-2y=-4 in slope intercept from.
y=0.5x+2
500
xWhich of the following equations do NOT represent linear functions?
A. 12 = 2x2 + 4y2 D. x = 9 - 3/4y
B. y = 3x +2 E. y = 5x/11
C. x = 8 F. x^2
A, C, F
500
Write the equation in slope-intercept form of the table below.
x 0 -1 2 5 8
y 1 -2 7 16 25
y = 3x + 1
500
You are at school, 12 miles away from home. You start walking home with your friends at a speed of 3 miles per hour towards your home.
a. Write an equation that represents your distance from home (y) after (x) hours.
b. How many hours does it take to get home?
a. y = -3x + 12
b. 4
500
Explain two ways you could solve 20 = 5(−3 + x)
1) Divide by 5 first, or (2) Distribute the 5 first