Linear Modeling
A gym charges a $10 sign-up fee and $25 per month. This is the total costs after 3 months.
Provide the linear model (equation) and total costs.
What is
y = 25x+10
$85?
This is slope-intercept form.
What is y = mx + b?
The vertical axis (line going up and down) on a coordinate grid.
What is the Y-axis?
The X value in the ordered pair for the y-intercept is always this number.
What is 0?
Put in slope-intercept form.
x - 4y = 8
Graph it.
y = 1/4x - 2
A phone company offers a plan where customers pay $50 per month plus $0.15 for every text they send. A customer sends 500 texts.
Write the linear model (equation) and give the total cost.
What is
Y = .15x + 50
$125
When putting the equation in slope-intercept form, you solve for this letter.
What is y?
This is the horizontal axis (going across) on a coordinate plane.
What is the x-axis?
This is the x-value that is plugged into a linear model.
What is an input value?
Put in slope-intercept form.
8x - 4y = 20
Graph it!
y = 2x - 5
A taxi ride costs $4 to start and $2.50 per mile.
This is the linear model (equation) and the total expense after a 15 mile ride.
What is
Y = 2.50x + 4
$41.50
Write an equation where the slope is 2 and the y-intercept is -5.
What is
Y = 2x - 5
When given an equation in slope-intercept form, Y = mx + b, the slope is represented by which letter?
What is the letter m?
This is the y-value that is produced after we plug in an x-value.
What is an output value?
Put in slope-intercept form.
3y - 2x = 9
Graph it!
y = 2/3x + 3
A student deposits $250 into their savings account. saves $100 each week from their part-time job. After 4 weeks this is their total savings.
Create a linear model (equation) and provide total savings.
What is
Y = 100x + 250
$650
A car rental company charges $50 per day plus a $100 flat fee. Write the equation that models the total cost (y) for (x) days.
Y = 50x + 100
When given an equation in slope-intercept form, Y = mx + b, the y-intercept is represented by which letter?
What is the letter b?
Slope is always considered a fraction, even when expressed as a whole number. This is the number we put under the whole number to make it a fraction.
Give an example.
What is the number 1.
example (many possible answers)
-6/1
Put in slope-intercept form.
6x – 2y = 10
Graph it!
y = 3x - 5
A car’s value decreases by $1,500 every year. It’s worth $25,000 now. In how many years will it be worth $10,000?
Express as a linear model (equation) and give the depreciation value.
What is
Y = 25,000 - 1,500x or 10,000 = 25,000 - 1,500x
10 years
Write in slope-intercept form
6x + 3y = 12
What is y = -2x + 4
This is the graph of the following equation
x - 4y = 8
Draw the graph on the whiteboards. Ensure the axis are labeled.
Hint: rewrite the equation first
Y = 1/4x - 2
Your graph should display a y-intercept of -2 and a slope of 1/4.
1. y must be by itself
2. the slope term (the part that has x) must go before the constant term (the stand alone number)
Put in slope-intercept form.
y + 9 = 2(x + 5)
Graph it!
y = 2x + 1