6th Grade Independent and Dependent Variables Test Solutions and Scoring (PDF)

6th Grade math test solutions: Independent and Dependent Variables – Maths PDF

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This variable relationships test answers for 6th Grade covers independent and dependent variables (Common Core 6.EE.C.9), with a free PDF to print.

Use this key to score the test out of 20 points. Each solution is fully worked, and the scoring line explains how to award each point and partial credit.

Grade 6 · Common Core State Standards: 6.EE.C.9

Variable relationships test answers: worked solutions

Question 1 – Variables [2 pts]

Independent: x (weeks). Dependent: y (cost).

$y = 8x$.

Scoring: 1 point for naming both variables; 1 point for the equation.

Question 2 – Complete the table [2 pts]

y = 8, 11, 13, 16.

Add 6 to each x.

Scoring: 1 point for two correct values; 2 points for all four.

Question 3 – Equation from a graph [2 pts]

The point $(1, 6)$ shows 6 cookies per box: $c = 6b$.

$6 \cdot 12 = 72$ cookies.

Scoring: 1 point for the equation; 1 point for 72 cookies.

Question 4 – Graph [2 pts]

(1, 2), (2, 4), (3, 6).

Points on y = 2x.

Scoring: 1 point for the correct pairs; 1 point for plotting them.

Question 5 – Read the graph [2 pts]

$y = x + 4$. When $x = 10$: $10 + 4 = 14$.

Scoring: 1 point for the equation; 1 point for 14.

Question 6 – Distance [2 pts]

$d = 12t$.

$54 = 12t$, so $t = 4.5$.

Scoring: 1 point for the equation; 1 point for 4.5 hours.

Question 7 – Match the equation [2 pts]

$e = s + 5$.

$8 + 5 = 13$ and $11 + 5 = 16$.

Scoring: 1 point for the equation; 1 point for both values.

Question 8 – Table and graph [3 pts]

(a) $p = 6h$. (b) $6 \cdot 7 = 42$, so $42.00. (c) The hours h are independent; the pay p depends on h.

The graph of p = 6h.

Scoring: 1 point for each part.

Question 9 – Compare relationships [3 pts]

Plan A: 4, 8, 12, 16. Plan B: 5, 6, 7, 8.

At x = 1, A costs 4 and B costs 5, so A is cheaper. At x = 2, 3, 4, A costs more.

Plan A is cheaper only when x = 1.

Plan A is cheaper only at x = 1.

Scoring: 1 point for each table; 1 point for the correct conclusion.

Total score

Total

20 points

Key facts behind this variable relationships test answers

Key facts

The independent variable is the input; the dependent variable is the output.
In y = kx, y is k times x and the graph passes through the origin.
In y = x + c, y is c more than x and the graph crosses the y-axis at c.
A table, a graph, and an equation can show the same relationship.
Use substitution to find y from x, and solve an equation to find x from y.

How to use this variable relationships test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 6 chapters: Grade 6 math.

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