Pre-Algebra Unit 10 Quiz Review Worksheet
The Coordinate Plane – Lesson 1
1) Identify, label, and draw the following on the blank coordinate plane below.
a. Label the x and y axis.
b. Label the origin.
c. Label quadrants I, II, III, and IV.
d. Using a ruler, draw a line passing through
𝟒
quadrants II and IV with a slope of - 𝟓.
e. Using a ruler, draw a line with an undefined
slope. Label this as line A.
f. Using a ruler, draw and label line B with zero
slope.
g. Label a point C somewhere on the x-axis.
h. Using a ruler, draw and label a line with the
equation x = -7.
i. Using a ruler, draw and label a line with the
equation y = 3.
Ordered Pairs as Solutions to Linear Equations – Lesson 1
2) Find a value of k that makes the ordered pair (-2, k – 2) a solution of the equation below. Show your work.
3y + 21x = 24
Graphing Linear Equations in Two Variables – Lesson 1
3) a. Solve the equation below for y. Show your work.
4y – 3x + 8 = 0
b. Create a table of values for your equation in part (a). Choose one (-) integer, zero, and one (+) integer
for values of x. Hint: Use values of x that result in integer (non-fraction) values of y.
c. Use the ordered pairs from part (b) above to carefully graph the equation from part (a) on the coordinate
plane below. Be sure you label your line and include arrowheads.
x
Substitution
y
(x, y)
d. Use rise over run to determine the slope of your line from question 5c.
e. If every point on your line that you graphed in part (c) were moved up 5 units, for example a point on a
different graph (-2, 4) would become (-2, 4 + 5) = (-2, 9), what would happen to the slope of your line?
Explain in a well-written sentence.
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Equations of Horizontal and Vertical Lines – Lesson 2
4) Determine whether the given equation represents a horizontal line, vertical line, or oblique line.
a. -4 + y = 4
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b. 5x - 3y = 15
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c. 21 = -7x
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d. -y = -1
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5) Write the equation of each of the given lines shown on the right and determine its slope.
Line a; Equation ______________, Slope ________
Line b; Equation ______________, Slope ________
Line c; Equation ______________, Slope ________
6) What is the equation of the y-axis?
y-axis; Equation ______________
7) What is the equation of the x-axis?
x-axis; Equation ______________
8) Identify two other points that lie on the line whose equation is x = -2.5.
(______, ______)
(______, ______)
Locating Intercepts and Using Intercepts to Graph Lines – Lesson 3
9) Determine the x and y intercepts and slope of each line below.
Line A
x – intercept = __________
y – intercept = __________
Slope = __________
Line B
x – intercept = __________
y – intercept = __________
Slope = __________
10a) Determine the x and y intercepts of equation below.
9y – 27x – 81 = 0
10b) Use your x and y intercepts to graph the line of the equation.
Use a ruler to draw your lines. Label your lines and include
arrowheads.
10c) Using rise over run, determine the slope of the line you
graphed in question 10b.
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11) A small submarine used to explore the ocean floor is at a depth of 3750 meters below sea level. The
submarine rises toward the surface at a rate of 30 meters per minute.
a. Write an equation where y represents the depth
of the submarine and x represents minutes.
b. Determine the x and y intercepts of your
equation from part (a). Show your work.
c. Use your intercepts in part (b) to graph your equation. Label your intercepts.
d. Use your equation to determine the depth of the submarine at 75 minutes. Show your work.
e. Within the context of this question, what do the x and y intercepts represent. Explain.
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12) A square-shaped floor space with a total area of 40,000 cm2 is going to be covered with tiles of two
different sizes. The first type of tile is square-shaped and has an area of 2500 cm2. The other type of
tile is rectangular-shaped and has an area of 1250 cm2.
a. Write an equation that represents the
different combinations of tiles that result
in a total area 40,000 cm2. Let x be the
large tiles and y be the small tiles.
b. Determine the x and y intercepts of your
equation from part a. Show your work.
c. Graph your equation using your answer from part b.
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Give your graph a title and label each axis.
Use an appropriate scale for each axis.
Using a ruler, lightly (with pencil) draw a line segment connecting your intercepts.
Draw points where your line segment passes exactly over where the grid lines meet.
Go back and erase your line segment but not your points.
d. Using your points from part c, find two other combinations of small and large tiles other than the x and y
intercepts that will result in a combined area equal to that of the area of the floor.
Combination #1 – Large Tiles _____________, Small Tiles _____________
Combination #2 – Large Tiles _____________, Small Tiles _____________
e. Verify by calculating that the combinations you listed in part (d) the total area of the floor to be tiled.
Show your work.
f. Explain why in this instance it is appropriate to only graph the points and not the line segment in
comparison to question 11 where you graphed the x and y intercepts and the segment between them.
Explain in a well-written sentence.
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Slopes of Lines – Lesson 4
Instructions – For questions 13 and 14, use the blank coordinate plane provided below.
13) Given a line containing the point (6, -2) and a slope
𝟏
of 𝟑, determine one other point on the same line.
Answer (_____, _____)
𝟓
14) A line with a slope of − 𝟐 contains the points
(-1, -3) and (x, 2). Determine the value of x.
15) The rise of a stair on a stairway is 17 cm. The height of the measured from the floor vertically to the top of
the stairs is 425 cm. A student determines that there must be exactly 23 steps in the stairway. Is this
correct? If so, why? If not, explain. Write your response in a well-written sentence.
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Practice Communication Question
16) In the space provided below, describe how the slope of a line describes its steepness. Use all of the
words in the vocabulary bank in your response. Your answer should be provided in at least 6 wellwritten and detailed sentences.
Vocabulary bank: undefined, rise, zero, positive, negative, run, ratio, vertical, horizontal, oblique
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Go to the next page and complete the extension question.
Practice Extension Question
17) A student is standing 180 feet from the base of a flagpole. Looking up, his line of sight to the top of the
1
flagpole has a slope of 5. If the distance from the student’s eyes to the ground is 60 inches, what is the
height of the flagpole? Show your work.