Page 108 - Math Course 3 (Book 1)

Writing Linear Equations
Mo. 3

Lesson 7 Write an Equation to Make a Prediction
Examples

KEY CONCEPTS:
1. Write equations given the slope and BUSINESS
y-intercept. The owners of the Good Times Eatery surveyed
2. Write an equation to make a prediction. their customers to find out where they lived. They
3. Write equations given a graph, a table, or two learned that for each 5-mile radius from their
points. restaurant, 30 fewer people visited them. They had
150 patrons in the area immediately surrounding
the diner. Predict the number of customers who
lived 20 miles away.
MO. 3 - L7a
Distance, Number of
Writing Equations: (mi), x Patrons, y
Slope and y-intercept 0 150

5 120
Let’s Begin 10 90

15 60

Write Equations From Slope and y-Intercept Explore
You know the rate of change of number of
Examples customers to each 5-mile radius (slope) and the
number of customers in the area immediately
surrounding the diner (y-intercept). Make a table of
Write an equation in slope-intercept form for the line. ordered pairs.

1 Plan
slope = – , y-intercept = 7
5 Write an equation to show the relationship between
the distance x and the number of customers y.
y = mx + b Slope-intercept form Then, substitute the distance of 20 miles into the
1 1 equation to find the number of customers.
y = – x + 7 Replace m with – and
4
4
b with 7 Solve
Step 1 Find the slope m.
1
Answer y = – x + 7 change in y decrease of 30 costumers
4
m =
change in x increase of 5 miles
–30
Write an equation in slope-intercept form for the line. m = 5

slope = 2, y-intercept = 0 m = –6 Simplify

y = mx+b Slope-intercept form
y = 2x + (0) Replace m with 2 and b with 0. Step 2 Find the y-intercept b.
y = 2x Simplify.
(x, y) = (distance, customers)
= (0, b)
Answer y = 2x
When the distance is 0 miles, the number of
customers is 150. So, the y-intercept is 150.

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