Point slope word problems
Mathematics
7th - 8th Grade
CCSS covered
Used 466+ times
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This quiz focuses on point-slope form equations and their real-world applications, targeting 7th and 8th grade mathematics students. The questions assess students' ability to calculate rates of change (slope) from given data points, write equations in point-slope form using the formula y - y₁ = m(x - x₁), and interpret linear relationships in contextual situations. Students must demonstrate mastery of coordinate geometry concepts, including identifying points on a line, understanding slope as a rate of change, and translating between verbal descriptions and algebraic representations. The problems require students to work with both positive and negative slopes, fractional rates, and various real-world scenarios such as altitude changes during hiking, profit calculations in business contexts, and distance-time relationships. Students need strong algebraic manipulation skills and the ability to distinguish between independent and dependent variables in practical situations. Created by a mathematics teacher in the US who teaches grades 7 and 8. This quiz serves as an excellent tool for assessing student understanding of linear functions and point-slope form after initial instruction on the topic. Teachers can use this as a formative assessment to identify areas where students need additional support, particularly in translating word problems into mathematical equations and recognizing the geometric meaning of slope and y-intercept. The quiz works effectively as a review activity before unit tests, as independent practice for homework assignments, or as a warm-up exercise to reinforce previously taught concepts. The varied question formats, including multiple choice options with common misconceptions, help teachers pinpoint specific areas of confusion. This assessment aligns with Common Core State Standards 8.F.B.4, which requires students to construct functions to model linear relationships, and 8.EE.B.6, which focuses on using similar triangles to explain slope concepts.
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6 questions
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1.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
A climber is on a hike. After 2 hours he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet.
What is the average rate of change?
What is a point-slope equation for the climber?
200 ; y - 700 = 200(x - 6)
75 ; y - 6 = 75(x - 700)
300 ; y - 700 = 300(x - 6)
75 ; y - 700 = 75(x - 6)
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
2.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
At 0 seconds, Mrs. Taylor was 10 feet off the ground. At 5 seconds, she was 20 feet off the ground. Write two point-slope form equations for the problem.
y - 0 = 2(x - 10)
y - 5 = 2(x - 20)
y - 0 = 5(x - 10)
y - 5 = 5(x- 20)
y - 10 = 2(x - 0)
y - 20 = 2(x -5)
y - 10 = 6(x - 0)
y - 20 = 6(x - 5)
Tags
CCSS.HSA.CED.A.2
CCSS.HSF.LE.A.2
3.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
11. Which of the following is NOT true about the graph of the line
y + 4 = -5(x - 1)
Tags
CCSS.HSA.CED.A.2
CCSS.HSA.REI.D.10
4.
MULTIPLE CHOICE QUESTION
3 mins • 1 pt
Find the rate of change.
Then write the point-slope equation.
-2 minutes per gallon
y - 80 = -2 (x - 10)
-20 minutes per gallon
y - 80 = -20 (x - 10)
-2 gallons per minute
y -80 = -2 (x - 10)
-20 gallons per minute
y - 80 = -20 (x - 10)
Tags
CCSS.HSF-LE.A.1B
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Write the equation of the line shown in point slope form.
Tags
CCSS.HSA.CED.A.2
CCSS.HSA.REI.D.10
6.
MULTIPLE CHOICE QUESTION
15 mins • 1 pt
Violet has an Internet business selling paint sets. After an initial website fee each week, she makes a profit of $0.75 on each set she sells. If she sells 8 sets and she makes $2.25; write an equation in point-slope form representing her weekly possible earnings.
Tags
CCSS.HSA.CED.A.2
CCSS.HSF.LE.A.2
CCSS.HSA.CED.A.1
CCSS.HSF.BF.A.1
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