📝 Making table of values for linear equation (14 MCQs)

📖 From Digital SAT Algebra • 4. Graphs • 14 questions available

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What is Making table of values for linear equation?

Definition:
Making a table of values for a linear equation involves creating a list of ordered pairs (x, y) that satisfy the equation by choosing arbitrary x-values, substituting them into the equation, and solving for the corresponding y-values, and this table provides a set of points that can be plotted to graph the line, showing the relationship between x and y.

Working:
To make a table of values, select a range of x-values (often including negative, zero, and positive), plug each x into the equation (e.g., $y = 2x - 1$ ), calculate y, and record the pairs in a table; usually, 3 to 5 points are sufficient to graph a straight line; for example, for $y = 2x - 1$ , if $x = -1$ , $y = -3$ ; if $x = 0$ , $y = -1$ ; if $x = 2$ , $y = 3$ ; the table is then used to plot the points and draw the line, ensuring accuracy.

Example:
A simple example is the equation $y = \frac{1}{2}x + 2$ ; choosing x = -2, 0, 2 gives y = 1, 2, 3 respectively, so the table is: (-2, 1), (0, 2), (2, 3); plotting these points and drawing a line through them graphs the equation, illustrating the method.

Reason:
Making a table of values is a fundamental technique for graphing linear equations, and it helps students understand the relationship between variables, practice substitution, and develop a systematic approach to graphing, making it an essential skill in algebra.

Easy

Medium

Hard

📝 All Making table of values for linear equation MCQs

Q1. For the equation $2x+y=8$ , a table contains $x=1,3,5$ . Which sequence correctly completes the corresponding $y$ -values?

6,4,2

✅

5,3,1

3,5,7

7,5,3

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: Substitute each given $x$ -value into $2x+y=8$ and solve for $y$ . When $x=1$ , $y=6$ ; when $x=3$ , $y=2$ ; when $x=5$ , $y=-2$ . Therefore, the correct sequence is $6,2,-2$ , so none of the listed choices match.

Q2. A student uses $3x-2y=12$ and records $x=0,2,4$ . Which completed table is correct?

y=-6,-3,0

y=6,9,12

y=-6, -3, 0

y=6,3,0

✅

💡 Difficulty: easy | ✅ Correct: D

📖 Explanation: Rearranging $3x-2y=12$ gives $y=\frac{3x-12}{2}$ . Substituting $x=0,2,4$ produces $y=-6,-3,0$ . This demonstrates that each table entry must satisfy the original equation, not merely follow an arithmetic pattern.

Q3. For $x+y=10$ , one table row contains $x=7$ and $y=3$ . A second row has $x=4$ . Which value should replace its missing $y$ ?

4

5

6

✅

14

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: Because $x+y=10$ , the missing value is found by subtracting the known $x$ -value from $10$ . For $x=4$ , $y=10-4=6$ . The pair $(4,6)$ satisfies the equation exactly.

Q4. A table is being constructed for $y=2x+1$ . One student says that increasing $x$ by $1$ should decrease $y$ by $2$ . What is the best evaluation of this claim?

A.It is correct because the coefficient is

2

B.It is incorrect because

y

increases by

2

✅

C.It is incorrect because

y

always stays constant

D.It is correct only when

x

is negative

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The coefficient of $x$ is $2$ , so every increase of $1$ in $x$ produces an increase of $2$ in $y$ . The student's error comes from reversing the direction of change. The relationship should be checked across consecutive table entries.

Q5. A table for $4x+y=20$ has $x$ -values $1,3,5,7$ . Which sequence of $y$ -values should appear, and why?

16,12,8,4

✅

4,8,12,16

19,17,15,13

20,16,12,8

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Solving for $y$ gives $y=20-4x$ . Substituting $x=1,3,5,7$ gives $16,8,0,-8$ , so the listed options actually contain an inconsistency. This highlights why every table value must be individually verified rather than selected by visual pattern alone.

Q6. A table for $5x- y=15$ contains the entries $(2, -5)$ , $(3,0)$ , and $(4,5)$ . A student claims the table is correct because the $y$ -values increase regularly. What is the strongest response?

A.The student is correct because equal differences prove the equation

B.The table is incorrect because the first pair does not satisfy the equation ✅

C.The table is incorrect because

x

must remain constant

D.The table is correct only for positive

y

-values

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Regular differences in a table do not prove that the pairs satisfy the original equation. For $(2,-5)$ , $5(2)-(-5)=15$ , so it actually does satisfy the equation; $(3,0)$ and $(4,5)$ also satisfy it. Thus the student's conclusion is valid, although the reasoning should include substitution.

Q7. A delivery company models total cost with $C=50+8m$ , where $m$ is the number of miles. If the table uses $m=2,5,9$ , which costs should be entered?

58,90,122

66,90,122

✅

58,90,82

100,250,450

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The fixed charge is $50$ , and each mile adds $8$ . Thus $C(2)=66$ , $C(5)=90$ , and $C(9)=122$ . The correct table must account for both the fixed starting cost and the mileage charge.

Q8. For $2x+3y=12$ , a student chooses $x=3,6,9$ and obtains $y=2,0,-2$ . Which statement best evaluates the table?

A.All three pairs satisfy the equation ✅

B.Only the first pair satisfies the equation

C.Only the second pair satisfies the equation

D.None of the pairs satisfy the equation

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Substitution confirms each pair: $2(3)+3(2)=12$ , $2(6)+3(0)=12$ , and $2(9)+3(-2)=12$ . The values also reveal a consistent relationship: increasing $x$ by $3$ decreases $y$ by $2$ .

Q9. A graph is known to contain the points $(0,6)$ , $(2,4)$ , and $(4,2)$ . A table is being created from the same linear relationship. Which additional point is most consistent with the pattern?

(5,1)

✅

(5,0)

(6,3)

(8,1)

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: From the listed points, every increase of $2$ in $x$ corresponds to a decrease of $2$ in $y$ . Therefore the relationship has slope $-1$ , giving $y=6-x$ . At $x=5$ , the corresponding value is $y=1$ , producing $(5,1)$ .

Q10. A table for $x-2y=6$ contains $x=2,6,10$ . One student writes $y=-2,0,2$ , while another writes $y=4,0,-2$ . Which student is correct?

A.The first student, because

y

increases as

x

increases

B.The second student, because every pair satisfies the equation

C.Both students are correct

D.Neither student is correct ✅

💡 Difficulty: hard | ✅ Correct: D

📖 Explanation: Solving $x-2y=6$ gives $y=\frac{x-6}{2}$ . Therefore the values are $-2,0,2$ for $x=2,6,10$ . The first student is correct, while the second reverses the sign for the nonzero values. Thus option A is the mathematically correct evaluation.

Q11. A graph shows a straight line passing through $(1,5)$ and $(3,1)$ . A student wants to complete a table using $x=5$ . Assuming the same linear relationship continues, what $y$ -value should be entered?

-1

-3

✅

3

9

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: From $(1,5)$ to $(3,1)$ , $x$ increases by $2$ while $y$ decreases by $4$ , giving a rate of change of $-2$ . Increasing $x$ from $3$ to $5$ decreases $y$ from $1$ to $-3$ .

Q12. A table for $3x+2y=18$ has $x=0,2,4,6$ . A student enters $y=9,6,3,0$ . Another enters $y=9,8,7,6$ . Which method should be preferred for verifying the correct table?

A.Choose the sequence with the larger values

B.Substitute every ordered pair into the original equation ✅

C.Choose the sequence with equal differences

D.Use only the first row because it is easiest

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Substitution directly tests whether each ordered pair satisfies the equation. For $3x+2y=18$ , the correct values are $9,6,3,0$ . Although equal differences can suggest a pattern, substitution provides stronger verification because it checks the actual relationship.

Q13. A school charges a fixed registration fee of $30$ dollars plus $12$ dollars for each activity. The table lists activity counts $0,2,4,6$ . Which sequence correctly models the total cost?

0,24,48,72

30,42,54,66

✅

30,36,42,48

12,30,48,66

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The cost model is $C=30+12a$ , where $a$ is the number of activities. Substituting $0,2,4,6$ gives $30,54,78,102$ , so none of the listed sequences is correct. This illustrates why the fixed fee must be included before comparing table patterns.

Q14. Suppose $y=7-3x$ . Two students complete a table using $x=1,2,3$ . Student A writes $4,1,-2$ , while Student B writes $10,13,16$ . Which conclusion is justified?

A.Student A is correct because

y

decreases by

3

✅

B.Student B is correct because

y

increases by

3

C.Both are correct for different forms of the equation

D.Neither is correct because

y

cannot be negative

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: Substituting $x=1,2,3$ into $y=7-3x$ gives $4,1,-2$ , exactly matching Student A. Student B appears to have used $7+3x$ , changing the sign of the coefficient. Negative values are valid solutions unless the problem imposes a restriction.

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