Vocabulary
Writing Linear Functions
Graphing Linear Functions
Slope
Intercepts
Modeling with Linear Functions
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
Write a linear function in slope-intercept form where slope is 3/4 and the y-intercept is -6
y=3/4 x-6
100
Which lists contains only points that line 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
Find the slope of the linear function
f(x)=2/3x
2/3
100
What are the x and y-intercepts of the following graph?
x-intercept: 2.5
y-intercept: -2
100
Mr. Toothaker gives out two pieces of candy to every student. Write a linear equation to model the number of candies he gives out as a function of the number of students.
y=2x
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
Is the following a linear function?
(2, 20)
(4, 16)
(6, 12)
(10, 4)
Yes, changes are proportional
200
The point (0, -5) is a point on the line:
y=1/2 x - 5
Name another point on the line.
Answers will vary. When put into the equation: y = 1/2 x -5, it needs the make a true statement.
200
Find the slope of a function where when the x-value is increased by 10, the y-value increases by 4
m = 2/5
200
What are the x and y-intercepts of the linear function:
4x+1/2y=8
x-intercept: 2
y-intercept: 16
200
Anthony is buying carrots and celery at the grocery store. The carrots cost $1.50 per pound and the celery costs $1.25 per pound. He has $10 to spend.
Write an equation in standard form to represent how he can split up his purchases.
1.5x+1.25y=10
300
Slope
the steepness of a graph
300
Write the linear function in this graph:
y=20x-15
300
The given table shows solutions to 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
What are the x and y-intercepts of the linear function
12x – 6y = –36
x-intercept:(-3,0)
y-intercept: (0,6)
300
Write an equation to model this situation: Maria wants to buy oranges and bananas at the store. Let x= number of oranges and y= the number of bananas. Oranges are $5 a pound and bananas are $4 a pound. She has a total of $20 to spend.
5x+4x=20
400
Slope-Intercept Form
=y coordinate
=slope
=x coordinate
=y intercept
400
Find the missing outputs
X | Y
0 | -3
1 | ?
2 | ?
3 | 9
1 and 5
400
for the equation y ≤ 2x + 1 would the test point (2,-2) create a true statement?
yes it will be in shaded region
400
What is the slope of
3x - 1/2y = 7 + 4x
y=-2x -14
Slope is -2
400
What are the x and y-intercepts of the linear function:
3y+5=5x-10
x-intercept: 3
y-intercept: -5
400
T-Mobile charges $100 a month for a family plan for four people, but that doesn't include the cost of the phone. Tiana buys a phone for $600 and splits the cost of the phone plan with her family of four. Write a function to show how much money she spends on her phone and plan after m months.
f(m)=25m+600
500
Standard Form
=integer
=x intercept
=integer
=y intercept
=integer
500
Put in slope-intercept Form:
3x + 2y = 8
y = (-3/2)x + 4
500
What is the slope of the linear function:
-8x + 4y = 12
2
500
Find the slope of the line that passes through the points (3, -2) and (-4, 6)
8/-7
500
What are the x and y-intercepts of a linear function in standard form?
Ax+By=C
x-intercept:
C/A
y-intercept:
C/B
500
You are 12 miles away from home when you are at school. You start walking home with your friends at a speed of 3 miles per hour.
a. Write an equation that represents your distance from home (y) after (x) hours.
b. What does the slope of the graph represent?
c. What is the y-intercept of the graph. What does this represent?
a. y=12-3x
b. 3 miles per hour
c. 12, the starting distance from home