C1L4 Notes
Lines
Find the slope of the line and interpret the slope.
1.
1
(-7H
1—>
A
change in y
Ay
y2~yi
change in x
Ax
X2~~ i
slope = -—s—- = — = ^-^x
Determine the slope of the line containing the points.
3. (5, -2), (-3, -4)
4. (-1, 4), (3, -5)
W:
YY\
-3~5
^z_
-^
5. (-*, 5), (-1,
6. (6, 4), (-3, 4)
^
o
^O
Graph the line containing the point P and having slope m.
7. P = (2,-l),m = 3
8. P = (-2,4),m =
<
9. P = (-2, -3), m = 0
1—I—I—I—I—h
10. P = (2, -5), m =undefmed
;
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V....
1—I—I—I—I—I—h
X
,\
pr- sucpe zauftnoti; M
Find an equation for the line with the given properties. Express your
answer using the general form and the slope-intercept form of the
equation of a line. QZM&tfrL. fotum
11. slope = 3; containing the point (-2, 5)
—4
12. slope = — ; containing the point (3, -4)
-n^Lce-Pr
13. x-intercept = -2; y-intercept = -7
a
-
__._
14. passes through the points (-3, 5) and (4, 7)
C,
15. slope = 3; y-intercept = 7 (0( 7
3x^9
7-0
16. slope = undefined; containing the point (8, -2)
17. Horizontal; containing the point (-3, 5)
18. parallel to the line y = 2x + 3; containing the point (4, 5)
. -
& PMUH^^
«?~N
y
- -3 -
19. parallel to the line x = -2; containing the point (2, 3
F7M
20. perpendicular to the line 3x + 4y = 8; containing the point (6, -1) / -3L
=0
21. perpendicular to the line y = 7; containing the point (-1,3)
-o
m
Find the slope and y-intercept of each line. Graph the line by hand.
= x- 6
23. -0.5x + 0.3y = 1.5
*;
<
1—I—I—I $ I—h
H—I—I—I—I—I—I
»
I/:
V
Find the x- and y-intercepts, then graph.
25. x - y 24. 5x + 2y = 12
"
i i> I I—i—i—i
26. A truck rental company rents a moving truck for one day by
charging $29 plus $0.20 per mile. Write a linear equation that relates the
cost C, in dollars, of renting the truck to the number x of miles driven.
What is the cost of renting the truck if the truck is driven 110 miles? 230
miles?
C,(iiq)~O.MG
= #57
5 ctxroF
f
27. The annual fixed costs for owning a small sedan are $1289, assuming
the car is completely paid for. The cost to drive the car is approximately
$0.15 per mile. Write a linear equation that relates the cost C and the
number x of miles driven annually.
28. The relationship between Celsius (°C) and Fahrenheit (°F) degrees of
measuring temperature is linear. Find a linear equation relating °C and
°F if 20°C corresponds to 68°F and 45°C corresponds to 113°F. Use the
equation to find the Celsius measure of 70°F.
70= Ate *- 32-
r&nfe**nte rtwr
7 5 70 F i
29. Commonwealth Edison Company supplies electricity to residential
customers for a monthly customer charge of $11.47 plus 11 cents per
kilowatt-hour for up to 600 kilowatt-hours.
a. Write a linear equation that relates the monthly charge C, in dollars,
to the number x of kilowatt-hours used in a month, 0 < x < 600.
* 0,ltK-t-/l,
b. Use a graphing calculator to graph the equation.
c. What is the monthly charge for using 200 kilowatt-hours?
C (3°°) -o.i( (zco) +//,
£& •;
= 33.
200 M
/S
d. What is the monthly charge for using 500 kilowatt-hours?
is
e. Interpret the slope of the line.
z £o$r iMo^fis^s 6V 4o.it
30. A cereal company finds that the number of people who will buy one
of its products in the first month that it is introduced is linearly related to
the amount of money it spends on advertising. If it spends $40,000 on
advertising, then 100,000 boxes of cereal will be sold, and if it spends
$60,000, then 200,000 boxes will be sold.
a. Write a linear equation that relates the amount A spent on advertising
to the number x of boxes the company aims to sell.
(tjoooo} 1 00000} ((*oooo} 200000)
-jooooo
x_ IOOOOQ - 5- (A - -
X-
_
# __ / ooooo
b. How much advertising is needed to sell 300,000 boxes of cereal?
£000°° ~£~ft~l OOOOC)
t/ooooo -THe
caryipfrNY
fnusr sP&JO / zoooo ON
-TO sou^ 300000 ftoxts OF
c. Interpret the slope.