The Graph of Ax + By = C 167
Lesson 3-3
11. a. Graph the line with equation 0x + 4y = 14.
b. Find two ordered pairs satisfying the equation.
c. Compute the slope of the line through the two points.
In 12 and 13, nd an equation for a line in standard form with the
given properties.
12. y-intercept
–
3 and slope 2
13. no y-intercept and passes through the point (17, 29.93)
14. Mallory combines
n
liters of a solution that is 3 mol/L chlorine
with y liters of a solution that is 5 mol/L chlorine. She ends up
with a mixture that contains 2 moles of chlorine.
a. Write an equation relating
n
, y, and the total amount of
chlorine in the mixture.
b. Graph the equation you obtained in Part a by fi nding the
n
- and y-intercepts. Consider
n
to be the independent
variable.
c. Use your graph to fi nd about how many liters of the 5 mol/L
solution Mallory must add to 0.4 liter of the 3 mol/L solution
to get the fi nal mixture.
15. Consider the graphs of Ax +
B
y = C and Ax +
B
y =
D
if A and
B are not both zero and C ≠
D
.
a. Rewrite each equation in slope-intercept form.
b. What is the relationship between the slopes of the lines?
What does that tell you about the lines?
c. What is the relationship between the y-intercepts of the lines?
What does that tell you about the lines?
d. Write the conclusions of Parts b and c as one
if-then statement.
e. Use the if-then statement from Part d to give the equations of
several lines parallel to 16x – 13y = 11.
16. Use a CAS expand command to show that multiplying the
equation Ax +
B
y = C by a nonzero number
k
yields another
equation in standard form. Why must this new equation describe
the same line as the original?
REVIEW
17.
At a library book sale, paperbacks are being sold for $0.50 each
and hardcover books are $1. If you want to buy
P
paperbacks
and
H
hardcover books, write a linear combination that
expresses the amount you will have to pay.
(Lesson 3-2)
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