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Algebra 1

3.2.3 Writing Linear Models without Technology

Algebra 13.2.3 Writing Linear Models without Technology

3.2.3 Writing Linear Models without Technology

3.2.3 • Writing Linear Models without Technology

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 questions 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.

1.

What is the initial amount of songs, or the y y -intercept of this situation?

2.

What is the slope, or rate of change?

3.

Write the equation of the linear model that represents the situation in slope-intercept form.

4.

How many songs will Marcus have in 8 months?

For questions 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, HH, in feet x x months since measurements began.

5.

What is the initial height of the tree, or the y y -intercept, when measurements began?

(Hint: Work each row backwards to where x = 0 x = 0 .)

6.

What is the slope, or rate of change?

7.

Write the equation of the linear model that represents the situation in slope-intercept form.

8.

What will the height of the tree be in 14 months?

Linear Models from Graphs

For questions 9 – 12, use the situation and graph below.

The graph models the cost in dollars, C C , of renting a tent at a campground for nn nights.

9.

What is the y y -intercept of the graph?

10.

What is the slope, or rate of change?

11.

Write the equation of the linear model that represents the situation in slope-intercept form.

12.

How much does it cost to rent a tent for 5 nights?

Self Check

The table below shows the revenue for the number of pizzas sold at a restaurant.

Which linear model could be used to predict the revenue if 4000 pizzas were sold?

y=80(4000) y=80(4000)

y=5(4000)+10 y=5(4000)+10

y=4000(10) y=4000(10)

I am not sure.

y= 1 5 (4000)+10 y= 1 5 (4000)+10

Additional Resources

Writing Linear Equations From Tables and Graphs

Linear Equations from Tables

The number of texts a teen sends, T T , in days, d d , is shown in the table below.

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 y y -intercept.

Since the value when d = 0 d = 0 is not present, work backwards to d = 0 d = 0 .

If d = 0 d = 0 was present, then T = 0 T = 0 since as each xx-value increases by 1, the y y -values increase by 65.

Step 2 - Find the slope of the situation.

Find the rate of change. The change in y y is 65 and the change in x x is 1, so the slope is 65

Step 3 - Write the equation in slope-intercept form.

y = m x + b y = m x + b

T = 65 d + 0 T = 65 d + 0

T = 65 d T = 65 d

Step 4 - Make a prediction.

Substitute d = 8 d = 8 into the equation.

T = 65 ( 8 ) = 520 T = 65 ( 8 ) = 520

After 8 days, the teen would have sent 520 texts.

Linear Equations from Graphs

The cost, C C , for the number of days, d d , 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 y y -intercept.

Since the value when d = 0 d = 0 is not present, work backwards to d = 0 d = 0 .

If d = 0 d = 0 was present, then C = 0 C = 0 since as each x x -value increases by 1, the y y -values increase by 35.

Step 2 - Find the slope of the situation.

Find the rate of change. The change in y y is 35 and the change in x x is 1, so the slope is 35

Step 3 -Write the equation in slope-intercept form.

y = m x + b y = m x + b

C = 35 d + 0 C = 35 d + 0

C = 35 d C = 35 d

Step 4 -Make a prediction.

Substitute d = 7 d = 7 into the equation.

C = 35 ( 7 ) = 245 C = 35 ( 7 ) = 245

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, F F , she can paint in h h hours.

How many square feet can Naomi paint in 8 hours?

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