Activity
Linear models can also be found by hand in some situations when the data follows a linear pattern since the slope remains the same between data points.
Linear Models from Tables
For 1 - 4, use the scenario and table below.
The table below shows the number of songs Marcus will have in his collection as he adds new songs each month.
Number of months, 0 1 2 3 Number of songs, 200 215 230 245
What is the initial amount of songs, or the -intercept of this situation?
200
What is the slope, or rate of change?
15
Write the equation of the linear model that represents the situation in slope-intercept form.
Compare your answer:
How many songs will Marcus have in 8 months?
320
Compare your answer:
For 5 - 8, use the situation and table below.
A new plant food is introduced to a young tree to test its effect on the height of the tree. The table shows the height of the tree, , in feet months since measurements began.
Number of months, 2 4 6 8 Height in feet, 13.5 14.5 15.5 16.5
What is the initial height of the tree, or the -intercept, when measurements began?
(Hint: Work each row backwards to where .)
12.5
What is the slope, or rate of change?
Write the equation of the linear model that represents the situation in slope-intercept form.
Compare your answer:
What will the height of the tree be in 14 months?
19.5
Compare your answer:
Linear Models from Graphs
For 9 - 12, use the situation and graph below.
The graph models the cost in dollars, , of renting a tent at a campground for nights.
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What is the -intercept of the graph?
30
What is the slope, or rate of change?
10
Write the equation of the linear model that represents the situation in slope-intercept form.
Compare your answer:
How much does it cost to rent a tent for 5 nights?
Compare your answer:
Self Check
The table below shows the revenue for the number of pizzas sold at a restaurant.
Number of Pizzas | 20 | 30 | 40 | 50 |
Revenue | 110 | 160 | 210 | 260 |
Which linear model could be used to predict the revenue if 4000 pizzas were sold?
I am not sure.
Additional Resources
Writing Linear Equations From Tables and Graphs
Linear Equations from Tables
The number of texts a teen sends, , in days, , is shown in the table below.
Days, | 1 | 2 | 3 | 4 |
Number of texts, | 65 | 130 | 195 | 260 |
Write an equation in slope-intercept form to represent the situation then predict the number of texts sent in 8 days.
Step 1 - Find the -intercept.
Since the value when is not present, work backwards to .
If was present, then since as each -value increases by 1, the -values increase by 65.
Step 2 - Find the slope of the situation.
Find the rate of change. The change in is 65 and the change in is 1, so the slope is 65
Step 3 - Write the equation in slope-intercept form.
Step 4 - Make a prediction.
Substitute into the equation.
After 8 days, the teen would have sent 520 texts.
Linear Equations from Graphs
The cost, , for the number of days, , a dog spends at doggie daycare is shown in the graph below.
Write an equation in slope-intercept form to represent the situation then predict the cost of a dog staying at doggie daycare after 7 days.
Step 1 - Find the -intercept.
Since the value when is not present, work backwards to .
If was present, then since as each -value increases by 1, the -values increase by 35.
Step 2 - Find the slope of the situation.
Find the rate of change. The change in is 35 and the change in is 1, so the slope is 35
Step 3 -Write the equation in slope-intercept form.
Step 4 -Make a prediction.
Substitute into the equation.
After 7 days, the cost of doggie daycare would be $245.
Try it
Try It-Writing Linear Equations From Tables and Graphs
Naomi is a professional painter. The table below shows how many square feet, , she can paint in hours.
Time in hours, | 1 | 2 | 3 | 4 |
Number of square feet, | 120 | 240 | 360 | 480 |
How many square feet can Naomi paint in 8 hours?
Compare your answer:
960
Step 1 - Find the -intercept.
Since the value when is not present, work backwards to .
If was present, then since as each -value increases by 1, the -values increase by 120.
Step 2 - Find the slope of the situation.
Find the rate of change. The change in is 120 and the change in is 1, so the slope is 120
Step 3 -Write the equation in slope-intercept form.
Step 4 -Make a prediction.
Substitute into the equation.
Naomi can paint 960 square feet in 8 hours.