Vocabulary
Graphing Linear Functions
Slope
Linear Functions Word Problems
Miscellaneous
100
Linear Function
Linear functions are those whose graph is a straight line.
A linear function has one independent variable and one dependent variable.
100
Which list contain points that lie on the graph of
y = 2x − 1?
a. (0, -1), (15, 29)
b. (-2, -4), (1, 3)
c. (-2, -3), (0, 0)
d. (2000, 1999), (3, 5)
a. (0, -1), (15, 29)
100
Identify the slope of the linear equation
y = -x + 6
The slope is -1
100
What are the two forms we have learned to write a linear equation?
Slope Intercept form
Standard form
100
What is another name for the x value?
Domain
input
independent variable
200
x-intercept and y-intercept
The x intercept is the point where the line crosses the x axis. At this point y = 0.
The y intercept is the point where the line crosses the y axis. At this point x=0
200
What is the y - intercept of the graph?
y = 0 or (0, 0)
200
Find the slope of a line that passes through the points (0, 5) and (2, 10)
m = 5/2
200
Anthony is buying carrots and celery at the grocery store. The carrots cost $1.50 per pound, x. The celery costs $1.25 per pound, y. He has a total of $10 to spend.
Write an equation in standard form that represents how many pounds of carrots x and pound of celery y that he can buy.
1.5x+1.25y=10
200
Solve the equation for x:
2(x + 3) = 14
x = 4
300
Slope
the steepness of a line
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
What is the slope of the linear function
y = 14
0
300
Maria wants to buy oranges and bananas at the store. Let x represent the number of oranges and y represent the number of bananas. Oranges are $5 a pound and bananas are $4 a pound. She has a total of $20 to spend.
Write an equation in standard form that represents the situation.
5x+4y=20
300
What is a key word for slope?
for each
every
per hour
(others that apply)
400
Slope-Intercept Form
=y coordinate
=slope
=x coordinate
=y intercept
400
Would (2,-2) be a solution to the inequality
y ≤ 2x + 1?
Yes because if (2, -2), then
-2 ≤ 2(2) + 1
-2 ≤ 4 + 1
-2 ≤ 5
Since this is true, (2,-2) is a solution.
400
Find the slope of a linear function that contains the points (-2 , 8) and (5 , -13)
m=(-13-8)/(5-(-2))=-21/7
m=-3
400
T-Mobile charges $100 a month for a family plan for four people. They also charge a one time set up fee of $25. Write a function to show how much money she spends in total after x months.
y=100x+25
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
Standard Form
500
How could you write this standard form equation in slope intercept form?
-2x + 3y = 12
y = 2/3x + 4
500
Write the equation of the table below.
x -1 2 5 8
y -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. What does the slope of the equation represent?
c. What does the y-intercept of the equation represent?
a. y = -3x + 12
b. 3 miles per hour - walking closer to home (it is negative since the distance is getting shorter)
c. 12 miles away from home (the starting point)
500
What are the type of solutions to an equation?
One solution, no solution, infinite solutions