Vocabulary
Writing Linear Functions
Graphing
Slope
Modeling with Linear Functions
100
Linear Function (2)
Graph is a straight line
Has an input, output, y-intercept, and slope
Modeled by y=mx+b
Has a constant rate of change
100
Write a linear function in slope-intercept form where m=3 and b=2
y=3x+2
100
Just by looking at the graph, how do you know if it is non-proportional?
It does not go through the origin and has a y-intercept that is not (0,0)
100
Find the slope of the proportional function
f(x)=2/3x
2/3
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
Y-Intercept (2)
On the y-axis
Has an x-value of 0
Also known as the initial value
The beginning of the story
200
Write a linear function with a slope of 9 and a y-intercept of -5
y=9x-5
200
The given table shows a proportional relationship between x and y.
What is the missing number in the table?
x 0 2 4 6
y -1 1 ? 5
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
Anthony is buying carrots and a melon at the grocery store. The carrots cost $1.50 per pound and the melon costs $1.25. He has $10 to spend.
Write an equation in slope-intercept form you could use to figure out the number of pounds of celery he can buy.
10=1.50x+1.25
300
Slope (2)
Steepness of a graph
vertical/horizontal
Also known as the rate of change
300
Write the linear function in this graph:
y=20x-15
300
What steps should you take to graph the line y=3x+2?
Option 1: put a point at (0,2) for the y-intercept and then count up 3, right 1 for the slope
Option 2: plug in values for x and solve for y, then plot them in the format of (x,y) on the graph
300
What is the slope of the linear function
y = 14
0
300
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
400
Slope-Intercept Form (describe all parts)
=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
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)
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
Leeroy is running up the stairs at 50 feet per minute and started at the ground floor. Kelvin is running down the stairs at 40 feet per minute and started 180 feet from the ground floor.
What equations would you use to represent this situation?
Leeroy: y=50x
Kelvin: y=-40x+180
500
Coefficient
The number in front of the variable
In the case of slope-intercept form, this would be the slope/rate of change
500
What is the equation of a line with a slope of 2 that runs through the point (-3, 4)
y=2x+10
500
What is the slope of the linear function:
-8x + 4y = 12
2
500
What is the equation for the table shown below?
x -4 0 4 8
y -1 2 5 8
y=(3/4)x+2
500
Leeroy is running up the stairs at 50 feet per minute and started at the ground floor. Kelvin is running down the stairs at 40 feet per minute and started 180 feet from the ground floor.
After how many minutes will the boys be on the same stair?
x=2
2 minutes