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Writing Equations

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This sample is an excerpt from one presentation on Writing Equations in Boardworks Middle School Math, which contains 179 interactive presentations in total.

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Information

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How to write an equation

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Graphing equations

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Constant speed

A car is traveling at a constant speed of 45 mph. Write an equation to show the relationship between the distance traveled in miles (d) and the time taken in hours (t).

How can we test this equation?

d = 45t

We can test the equation by substituting 1 for t.

We know the car is traveling 45 mph, so the equation works.

45 × 1 = d45

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Distance/time graph

x

y

Time (t), hours

Distance/time

We can substitute more values for t to create a table.

We can graph these pairs of values on a coordinate plane.

We can use our equation (d = 45t) or the graph to find other values on the line.

a) Find d if t = 3. d = 135 milesb) Find d if t = 21. d = 945 miles

Time (t)Distance (d)

10450

8360

6270

4180

290

For example:

450

270

180

90

0 2 6 8 10

360

4

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Calculating cost

Maria is ordering books online. Each book costs $8. There is an additional $3 charge for shipping and handling. Write an equation showing the relationship between the number of books Maria orders (b) and the total cost (c).

The total cost will be $8 per book, plus $3 for shipping.

How can we represent this mathematically?

c = 8b +3

How can we graph this equation?

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20

Graphing cost

x

y

Number of books (b)1 3 4 5

10

30

40

50

0 2

Cost/books

Once again, we can use substitution to find value pairs.

Why doesn’t the line pass through the origin?

Try substituting 0 for b. What value do you get for c?

No. of books (b)Total cost (c)

543

435

327

219

111

c = 8(0) + 3 = 3

What does this mean in the context of the problem?

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Test your knowledge!

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