Chapter 7 7.1 Slope-Intercept Form Worksheet - Mhr Page 6
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17Solution
Rearrange the equation into the form y = mx + b. To do this,
a)
isolate the variable y.
3x - 2y - 600 = 0
3x - 600 = 2y
3x - 2y - 600
+ 2y
= 0
+ 2y
Dividing all terms by 2
3x - 600 = 2y
_
_
_
2y
3x
600
_
3
gives
.
-
=
x - 300 = y
2
2
2
2
_
3
_
So, y =
x - 300.
The equation written in slope-intercept form is y = 3
2
x - 300.
2
_
The slope of the line is 3
or 1.5. It represents income of $1.50
b)
2
per ball. The slope is positive because the money is coming in.
The y-intercept is -300. It represents a cost of $300 to rent the
c)
portable dunk tank. It is negative because the money is paid out
as an expense.
At the break-even point, students do not make or lose money.
d)
So, the profi t is zero.
Substitute y = 0 into the equation and solve for x.
_
y = 3
x - 300
2
_
= 3
0
x - 300
2
_
= 3
300
x - 300
+ 300
2
_
1
3
(
)
2(300) =
2
x
2
1
600 = 3x
200 = x
To reach the break-even point, they must sell 200 balls, at a rate
of $1.50 per ball. They will make money if they sell more than
200 balls. They lose money if they sell fewer than 200 balls.
Your Turn
Parents of members of the cheerleading squad rent a hall. They
arrange a talent show as a fundraiser. The relationship between
the number of tickets sold, x, and the profi t, y, in dollars, may be
represented by the equation 12x - y - 840 = 0.
What is the slope of the line? What does the slope represent?
a)
Identify the y-intercept. What does it represent?
b)
How many tickets must the parents sell to reach the
c)
break-even point?
345
7.1 Slope-Intercept Form • MHR
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