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 standard form and slope-intercept form where A=2 B=-4 and C=19
2x-4y=19 y=1/2 x-19/4
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 proportional 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. Garvey gives out two pages of homework to every student. Write a linear equation to model the number of pages he has to print 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
Write a linear function with a slope of -9 and a y-intercept of 5
f(x)=-9x+5
200
What is the equation of the line that is parallel to 2x – 3y + 11 = 0 going through (2,–1)
.y=(2/3)x-(7/3)
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 a directly proportional relationship between x and y.
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
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
Write a linear function that contains the points (0,2) and (-4,5).
f(x)=3/4x +2
400
for the equation y ≤ 2x + 1 would the test point (2,-2) create a true statement?
yes it will be shaded in
400
Find the slope of a linear function that contains the points (-2.5 , 9) and (5 , -13.5)
m=(-13.5-9)/(5-(-2.5))=-22.5/7.5
m=-3
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
Find the line Perpendicular to 3y – 2x + 11 = 0 going through (2,–2)
y = (-3/2)x + 1
500
What is the slope of the linear function:
-8x + 4y = 12
2
500
The table shows values for What is an equation for f(x)?
x -1 3 7 11
y -8 -5 -2 1
f(x)=(3/4) x - (29/4)
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 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.(Standard Form)
b. Find the slope of the graph. What does this represent?
c. Find the y-intercept of the graph. What does this represent?
a. 3x+y=11
b. 3 miles per hour
c. 11 the starting distance from home