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Unformatted text preview: Solutions to Quiz 11A
www.math.uﬂ.edu/˜harringt
October 27, 2007
1. Let x = 5 be the line L.
(a) Find the slope of a line that is parallel to L.
m = undeﬁned
(b) Find the slope of a line that is perpendicular to
L. m = 0
Note: To see why, please graph x = 5.
2. Find the equation for the line containg the xintercept 2 and the yintercept 3. Write your answer in slopeintercept form.
METHOD 1:
With xintercept 2 and yintercept 3, we know that the line contains
the points (0, 3) and (2, 0). Now we can ﬁnd the slope.
m= ∆y
3
3
=
=−
∆x
−2
2 Hence, y = −3 x + b. Since we already know that the yintercept is 3,
2
then, b = 3. So, y = −3 x + 3.
2 METHOD 2:
The studious student could recall from the homework on page 193 number 82 that
xy
+ =1
ab 1 where a is the nonzero xintercept and b is the nonzero yintercept.
Thus, we have the following:
xy
+
=1
23
y
x
= − +1
3
2
2
y = − x+3
3
3. Determine the validity of each statement.
(a) ”Every line has two distinct intercepts.”
This statement is FALSE. Consider the line y = 3. This line only
has one intercept namely, the yintercept (0, 3).
(b) ”Perpendicular lines have slopes that are reciprocals of one another.”
This statement is FALSE. The correct statement should read
”Perpendicular lines have slopes that are NEGATIVE reciprocals
of one another.”
(c) ”A system of equations containing two variables always has a least
one solution.”
This statement is FALSE. Consider the following system:
y =x+3
y =x+5
This system has no solution. (Why?) So a system of two variables
does not always have at least one solution. 2 ...
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This note was uploaded on 07/12/2011 for the course MAC 1140 taught by Professor Williamson during the Fall '08 term at University of Florida.
 Fall '08
 WILLIAMSON
 Calculus, Algebra, Slope

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