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This page shows questions in the Math 8 Reasoning public release module at MSDE. 8th Grade Math
"Math 8 Reasoning"

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This is a test question that allows you to enter extended text in your response.

Two rival companies began the same year. The equations below model the number of employees, y, at these companies x years after the companies began.

Company R: y equals 3 x plus 24

Company T: y equals 4 x plus 10

Company R stated, "We have 42 employees, the same number of employees as company T has this year." Determine if company R's claim is possible. Explain your reasoning.

Company T stated, "After 15 years, we will have the same number of employees as company R." Determine if company T's claim is possible. Explain your reasoning.

Enter your answers and your explanations in the space provided.

Copyright 2023, New Meridian Corporation. Reprinted with permission. All rights reserved. The printing, copying, redistribution, or retransmission of this content without express written permission is prohibited.

This is a question with 2 parts, including a multiple choice question that allows you to select only one option, and, a test question that allows you to enter extended text in your response.

The equation of line s is y equals negative 3 x plus 2.

The equation of line t is y equals one half x minus 3.

Line s and line t form a system of equations. The solution to the system of equations is located at point P.

Part A

Which graph correctly shows line s, line t, and point P?

  1. A.
    Line s and line t are plotted on a coordinate plane with x and y axes ranging from negative 9 to 9 in increments of 1. Line s begins at a little less than negative 2, 9, goes down through the points negative 1, 5; 0, 2; and 1, negative 1. It ends with an arrow at a point midway between three and four, negative 9. Line t begins at a point negative 9, midway between negative 7 and negative 8, goes up through the points negative 6, negative 6; negative 2, negative 4; and four, negative 1. It ends with an arrow at the point 9, midway between 1 and 2. Point P is plotted at the intersection of lines s and t, at a point midway between 1 and 2, a little less than negative 2.
  2. B.
    Line s and line t are plotted on a coordinate plane with x and y axes ranging from negative 9 to 9 in increments of 1. Line s begins at a little less than negative 2, 9, goes down through the points negative 1, 5; 0, 2; and 1, negative 1. It ends with an arrow at a point midway between three and four, negative 9. Line t begins at a point negative 9, midway between negative 7 and negative 8, goes up through the points negative 6, negative 6; negative 2, negative 4; and four, negative 1. It ends with an arrow at the point 9, midway between 1 and 2. Point P is plotted on line t at the point 0, negative 3.
  3. C.
    Line s and line t are plotted on a coordinate plane with x and y axes ranging from negative 9 to 9 in increments of 1. Line s begins at a little less than negative 2, 9, goes down through the points negative 1, 5; 0, 2; and 1, negative 1. It ends with an arrow at a point midway between three and four, negative 9. Line t begins at a point negative 3, negative 9, goes up through the points negative 1, negative 5; 2, 1; and 5, 7. It ends with an arrow at the point 6, 9. Point P is plotted at the intersection of lines s and t, at the point 1, negative 1.
  4. D.
    Line s and line t are plotted on a coordinate plane with x and y axes ranging from negative 9 to 9 in increments of 1. Line s begins at a little less than negative 2, 9, goes down through the points negative 1, 5; 0, 2; and 1, negative 1. It ends with an arrow at a point midway between three and four, negative 9. Line t begins at a point negative 3, negative 9, goes up through the points negative 1, negative 5; 2, 1; and 5, 7. It ends with an arrow at the point 6, 9. Point P is plotted on line t at the point 0, negative 3.

Part B

Can an equation of a line share more than one solution with line s?

  • If yes, explain your reasoning and provide an example of an equation.
  • If no, explain your reasoning and list any assumptions that you have made.

Enter your answer and your explanation in the space provided.

Copyright 2023, New Meridian Corporation. Reprinted with permission. All rights reserved. The printing, copying, redistribution, or retransmission of this content without express written permission is prohibited.