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1. Consider a line segment AB with endpoints A(−3, 2) and B(3, −6).
(a) (2 points) Find the distance between the two points.
(a)
(b) (2 points) Find the midpoint of the line segment AB.
←→
(c) (2 points) Find the slope of the line AB.
(b)
(c)
(d) (2 points) Graph the line segment AB. Show the rise and run of the slope.
y
Page 1 of 4
Study Guide 1
Total Points: 50
2. (8 points) Graph both linear equations in each system, clearly mark intercepts,
rise and run of the slope, or any point used in the graph:
3x − 4y = 12
4x + 3y = −12
2x + 5y = 10
2x + 5y = −10
y
y
x
x
3. Consider a line segment AB with endpoints A(−5, 1) and B(1, 3).
(a) (2 points) Find the distance between the two points.
(a)
(b) (2 points) Find the midpoint of the line segment AB.
←→
(c) (2 points) Find the slope of the line AB.
(b)
(c)
Page 2 of 4
Study Guide 1
Total Points: 50
4. (8 points) Graph both linear equations in each system, clearly mark intercepts,
rise and run of the slope, or any point used in the graph:
y = 35 x − 3
y = 34 x + 2
y = 5x + 3
y=
−4
3
3 x−2
y
y
x
x
←→
5. Find the slope of line AB that contains the points A(−3, 5) and
(a) (2 points) B(3, −2).
(a)
(b) (2 points) B(7, 5).
(b)
(c) (2 points) B(−3, 0).
(c)
Page 3 of 4
Study Guide 1
Total Points: 50
6. (6 points) Graph both linear equations in each system, clearly mark intercepts,
rise and run of the slope, or any point used in the graph:
y − 2=
2
5
f
(x + 2)
x=2
y+4 =0
y
y
x
x
7. Algebra Review Problems:
(a) (2 points) Solve 3(x − 5) + 2 = 7 − 2x.
(a)
( )2
(b) (2 points) Simplify x3 · x4 by using exponential rules.
(b)
(c) (2 points) Solve −3 < 2x + 1 ≤ 7, then graph the solution.
-4
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
(d) (2 points) Multiply (2x − 4)(2x + 4) using FOIL method.
3
3
(d)
Page 4 of 4
Study Guide 1
Total Points: 50
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