# data[].attributes.body
Word Problem:

Aurora wants to move into a new house. The house cost $1,200 and rent is $300 a month. The other house cost $3,000 with $100 a month. Which house is cheaper?

Equation:

house #1

y=300x+1,200

house #2

y=100x+3,000

The second house is cheaper you don't even have to solve it because the rate of change for the second is cheaper so it will start out more expensive then the first house but then slowly House #2 will be greater.

# data[].attributes.body
Linear Functions-

Linear functions have to be in a straight line and they CAN be proportional

They have a constant rate of change.

Linear functions have one independent variable and one dependent, which means y depends on x.

Y= mx+b

M= Slope/rate of change

B=y-intercept

When x is 0 what is y and that is initial value.

"A positive rate of change indicates that a linear equation"

"A negative rate of change indicates that a linear line is decreasing"

# data[].attributes.body
Equation: y=3x+5

3 is the slope and 5 is the y intercept.

You can represent this in a table as well. For every same in change in x there is a constant change in the y- value

# data[].attributes.body
Linear equation: Its an equation between two variables that makes a straight line when you plot it in the graph.

Ex. y=2x + 1

a linear function has to be a straight line.

it can be used in a table and graph the equation of linear function.

Equation:

y=mx +b

m= rate of change

b= y-intercept

# data[].attributes.body
graph:

in a straight line

passes through the origin( not always true)

equation:

y=mx+b

m=rate of change

b= y-intercept

table:

when there's one input there's always one output

when input value is zero, the output value is the y-intercept

other facts:

constant rate of change

slope

steepness

It has one independent and one dependent.

input=domain

output=range

word problem:

Portia went to a company store last week. She has to pay a monthly fee of $10 plus an additional fee of $5. How much would she have to pay in total for 12 months?

# data[].attributes.attachment_link.description
Varsity Tutors connects you to top tutors through its award-winning live learning platform for private in-home or online tutoring in your area.

# data[].attributes.body
Kim and Cyndi are starting a business tutoring students in math. They rent an office for $400 per month and charge $40 per hour per student.  If they have 15 students each (meaning Kim has 15 and cyndi has 15 so they have 30 altogther) for one hour per week how much profit do they make together in a month? (assume 4 weeks per month)
The starting point is -400 in a month since they have to pay that much. they charge $40 per student per hour meaning 1 student pays $40 for one hour. They have 15 students each, so its 30 students. To get that amount of money for 1 week, you'd multiply 30 and 40, which 1,200. To get how much they'll earn in a month, multiply 1,200 and 4 to get 4800. Since they started at -400 you would have to subtract 400. The answer would be 4,400 per month. the expression would be 160x is the revenue (the money coming in) and the expense (money they have to spend) is 400 so the equation for profit inone month would be y= 160x-400

# data[].attributes.body
Linear functions have to be a straight line

They have to follow the equation Y=mx+b

In this picture b=0 (when this happens we put the equation as y=mx) and m=2

# data[].attributes.body
A function relates an input to an output.

A linear function is a straight line on a graph.

For every linear function, there is an equation: Y=mx+b or Y=mx.

A linear function can be proportional, but it does not have to be.

Word problem:

Patricia wants to join a dating site. The new members fee is $20 and then $12.50 per month. If she uses the site for a year and 2 months how much money has she paid?

# data[].attributes.body
A linear function on a graph is a straight line. y = f(x) = Mx + b. A linear function has one independent variable (x) and one dependent variable (y)

equation: y=3x + 4

3 is the constant rate and 4 is the initial value

# data[].attributes.body
for the same change in x value there is a constant rate for the y value

own equation: y= 4x+3

4 is the constant rate and 3 is the initial value (y intercept)

how to check if the point (2,6) is on the graph below.

y=mx+b

6=2x+2 y=6

x=2