Vocabulary
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
Is the table a function? Justify your answer.
x -1 4 5 -1 8
y -7 3 2 -6 6
No. The table is not a function because there are two different y-values when x is equal to -1.
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 is the y-intercepts of the following graph?
b=-2
100
What are the two forms we have learned to write a linear equation?
Slope-Intercept form
Standard form
200
y-intercept
What is the x-value?
The y-intercept is the y-coordinate where the line intersects the y axis. At this point x=0.
200
Does the set of points represent a function? Explain.
(-4, 0), (-2, 1), (0,8), (2, 1), (3, -1)
Yes. The set of points represent a function because each x-value only has one y-value.
200
Would (3,-2) be a solution to the equation
y = 2x + 1?
No, because...
y=2x+1
-2 = 2(3) + 1
-2 = 6 + 1
-2 = 7
Since this is false, (3,-2) is not a solution.
200
Use the slope formula to find the slope of a line that passes through the points (0, 5) and (2, 10)
m = 5/2
200
What is the y-intercept?
x -6 -2 6 10
y -6 -4 0 2
b=-3
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
300
Slope
the steepness of a line
300
Determine if the relationship is a linear function. Justify your answer. If the relationship is linear, then write the equation in y=mx+b form.
Yes. The graph is a function because each x-value only has one y-value. The graph passes the vertical line test. The relationship is linear because the data forms a straight line graphically.
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 16
y 0 1 ? 8
2
Note: y is proportional to x because the ratio y/x is constant.
300
What is the slope of the linear function
y = 14
m=0
300
What is the coordinate of the y-intercept?
12x – 6y = –36
y-intercept coordinate: (0,6)
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
400
Slope-Intercept Form
=y coordinate
=slope
=x coordinate
=y intercept
400
Determine if the relationship is a linear function. Justify your answer. If the relationship is linear, then write the equation in slope-intercept form.
x -4 0 4 12 20
y 5 2 5 11 17
Yes. The table is a function because each x-value only has one y-value. The table is linear because the rate of change is constant.
y=3/4x+2
400
Graph the function on graph paper.
y=-1/2x+9
Look at the graph paper.
m=-1/2
b=9
400
Look at the graph on a separate slide on Schoology. Use the formula to calculate the slope. Identify the y-intercept. Finally, write the equation of the line.
m=-2
b=2
y=-2x+2
400
What are the x and y-intercepts of the linear function:
-10x + 6y = -30
x-intercept: 3
y-intercept: -5
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
500
Standard Form
=integer
=x intercept
=integer
=y intercept
=integer
500
Write the equation of the line in slope-intercept form and then find the missing coordinate given that the slope is -2 and goes through both points at (-1,k) and (3,0).
y=-2x+6
k=8
500
Graph the function on graph paper.
-8x + 4y = 12
Look at the graph.
m=2
b=3
500
Write the equation of the table below.
x -1 2 5 8
y -2 7 16 25
y = 3x + 1
500
Identify the slope and y-intercept of the standard form equation
-5x + 3y = -15
Slope intercept form y = (5/3)x - 5
m=5/3
b=-5
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)