Vocabulary
Writing Linear Functions
Graphing Linear Functions
Slope
Linear Functions Word Problems
Mystery!
100
Describe a y-intercept.
The y intercept is the point where the line crosses the y axis. At this point x=0
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 function because x and y have a constant rate of change.
100
Identify the slope of the linear equation.
y= -x - 6
The slope is -1
100
Write the slope-intercept form equation using function notation.
f(x)=mx+b
100
Is this a function, relation, both, or neither?
(-2,3), (-1,3), (8,4), (11,2)
Both
200
Describe an x-intercept.
The x intercept is the point where the line crosses the x axis. At this point y = 0.
200
Write the linear function for a slope of -1/2 and a y-intercept of -3.
y=-1/2x - 3
200
What's the slope for the line x=4?
The slope in undefined
200
What is the slope for the graph of y=-3
The slope is 0 because this is a horizontal line.
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 = -10
300
What does slope measure?
The steepness of a line
300
Write the linear function of this graph:
y=20x-15
300
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. When graphed, it creates a straight line.
300
Write a linear function (using function notation) for this situation. A pizza place charges $7 for a large pizza and $1 for each additional topping.
f(x)=x+7
300
Graph y=4
400
What's the equation for Slope-Intercept Form
y=mx+b
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.
Find F(73) when y=3x+2050
F(73)=$2,269
400
Use algebra to rewrite this equation into slope-intercept form.
-5x + 3y = -15
y = 5/3x - 5
500
Define a linear function.
A function whose graph is a nonvertical line and has a constant rate of change
500
Use algebra to write x-2y=-4 in slope intercept from.
y=1/2x+2
500
Which of the following equations do NOT represent linear functions?
A. 12 = 2x2 + 4y2 D. x = 9 - 3/4y
B. y - x + 3 + x E. y = 5x/11
C. x = 8 F. xy = 9
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) UNDO: Divide by 5 first, or (2) REWRITE: Distribute the 5 to (-3+x)