Math 135 - Linear Equations Worksheet With Answers - University Of Hawaii At Manoa - 2014 Page 2
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1
2Math 135
Linear Equations
Worksheet Solutions
(b) Find the equation of a perpendicular line through (2 4).
1
1
14
4 =
(
2) or
=
+
3
3
3
5. Consider the line 3
2 = 6.
(a) Find the slope and intercepts of the line.
3
slope is
,
intercept is (2 0), and
intercept is (0
3)
2
(b) Find a point on the line and a point not on the line.
Answers may vary. Check that a point on the line agrees with the given equation,
while a point not on the line does not.
(c) Write the equation of the line in slope-intercept form.
3
=
3
2
6. Find the point of intersection of the graphs of
+ 3 =
24 and
+ =
8.
(0
8)
7. Solve:
= 3 + 2
3 + 6
= 12
(0 2)
8. Write down a system of two linear equations that has
(a) Exactly one solution
Any pair of non-parallel lines.
(b) No solution
Any pair of parallel lines.
(c) Infinitely many solutions
Any pair of lines whose equations could be reduced to the same equation.
9. Derive the point-slope form of the equation for a line by following these steps.
Step 1: Let
be the line passing through the fixed point (
) and an arbitrary
1
1
point (
).
Step 2: Manipulate the general formula for the slope of .
1
=
=
=
(
)
1
1
1
University of Hawaii at Manoa
Spring 2014
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