Mathematics 8 Reviewer Q2

Which of the following is a linear inequality in two variables?

• 3x + y < 5

• y = 5x - 8

• 3x + y = 3

• 5x = y + 9

Answer explanation

The correct choice, 3x + y < 5, is a linear inequality because it involves a less than sign. The other options are either equations or do not represent inequalities.

The daily school allowance of Jean (j) is less than the daily school allowance of Gwen (g). Which of the following mathematical statement represent the given situation?

• j ≠ g

• j = g

• j > g

• j < g

Answer explanation

The statement "Jean's daily allowance is less than Gwen's" translates mathematically to j < g, indicating that Jean receives a smaller allowance than Gwen.

Which of the following does NOT represent the graph of linear inequality in two variables?

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Given the system of linear inequalities y < -x + 5 and y > x - 2, which of the given points is part of the solution set of the graphs of systems of linear inequalities?

• (6, 3)

• (0, 0)

• (7, 2)

• (8, 4)

Answer explanation

To check if (0, 0) is a solution, substitute into the inequalities: 0 < -0 + 5 (true) and 0 > 0 - 2 (true). Both inequalities are satisfied, so (0, 0) is part of the solution set.

Which process is wrong in solving the systems of linear inequalities in two variables?

• Find the x-intercept and y-intercept.

• Plot the points.

• Use a solid line if the inequality symbol is <,> and a broken line if the inequality symbol is ≤,≥

• Use a test point to determine the shaded region/solution set of the systems of linear inequality.

Answer explanation

The correct choice is to use a solid line for ≤,≥ and a broken line for <,>. The opposite is stated in the incorrect option, which confuses the line types based on the inequality symbols.

In how many point(s) does a vertical line intersect the graph of a function?

• at least one point

• at exactly one point

• more than one point

• at exactly two points

Answer explanation

A vertical line intersects the graph of a function at exactly one point because a function has only one output for each input. Therefore, the correct answer is 'at exactly one point'.

Which of the following sets of ordered pairs represents a function?

• {(0,2), (1, 3), (2, 4), (3, 5)}

• {(0,2), (1, 3), (1, 4), (3, 5)}

• {(0,1), (0, 2), (0, 3), (0, 4)}

• {(0,0), (4, 2), (4, -2), (9,3)}

Answer explanation

The set {(0,2), (1, 3), (2, 4), (3, 5)} represents a function because each input (first element) is unique. The other sets have repeated inputs, which violate the definition of a function.

Given the set of ordered pairs {(1, a), (2, v), (3, z), (4, d)}, what is the domain?

• a, v, z, d

• 1, 2, 3, 4

• 1, a, 2, v

• 3, z, 4, d

Answer explanation

The domain of a set of ordered pairs consists of the first elements. In this case, the first elements are 1, 2, 3, and 4, making the domain {1, 2, 3, 4}. Thus, the correct answer is 1, 2, 3, 4.

Which of the following graphs has positive slope?

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Danny works as delivery boy in a water refilling station. His monthly salary is represented by the function 1.50x + 6,000. What table of values best describe the total monthly earnings 𝑓(𝑥) of Danny in terms of the number of gallons x he delivered for the whole month?

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