Proportional Relationships Test Prep Guide

You've learned proportional relationships. The test is tomorrow. Here's exactly what you need to review.

Test Checklist

Before the test, make sure you can do each of these:

1. ✅ Identify proportional relationships from tables
2. ✅ Identify proportional relationships from graphs
3. ✅ Identify proportional relationships from equations
4. ✅ Find the constant of proportionality
5. ✅ Write the equation $y = kx$
6. ✅ Compare two proportional relationships
7. ✅ Solve proportional relationship word problems
8. ✅ Interpret the meaning of $k$ in context

Skill 1: Table Test (Almost Guaranteed)

Given a table, determine if it's proportional.

Method: Divide $y$ by $x$ for every row. If all answers match, it's proportional.

Practice table:

| $x$ | $y$ | | :-: | :-: | | 2 | 5 | | 6 | 15 | | 8 | 20 |

$5 \div 2 = 2.5$, $15 \div 6 = 2.5$, $20 \div 8 = 2.5$. All match. $k = 2.5$. Equation: $y = 2.5x$. Proportional.

On the test: Expect 1-2 table questions. Some will ask for $k$ or the equation.

Skill 2: Graph Test

Given a graph, determine if it's proportional.

Method: Check two things:

1. Is the graph a straight line?
2. Does the line pass through $(0, 0)$?

If yes to both, it's proportional.

Pro tip: If the graph is a straight line but the origin isn't labeled, look for a point where $x = 0$. If $y \neq 0$, it's not proportional.

Skill 3: Equation Test

Given an equation, determine if it's proportional.

Method: Can the equation be written as $y = kx$ with no added constant?

• $y = 8x$ — proportional ($k = 8$)
• $y = \frac{1}{2}x$ — proportional ($k = \frac{1}{2}$)
• $y = 3x + 2$ — not proportional
• $y = -4x$ — proportional ($k = -4$)
• $y = x$ — proportional ($k = 1$)

Skill 4: Find the Constant of Proportionality

This is the single most tested skill. Given a table, graph, equation, or word problem — find $k$.

| Given | How to find $k$ | |---|---| | Table | Divide $y$ by $x$ | | Graph | Pick a point, divide $y$ by $x$ | | Equation | The coefficient of $x$ | | Word problem | The rate per 1 |

Skill 5: Write the Equation

Once you have $k$, write $y = kx$.

Example: A table gives $k = 4$. Equation: $y = 4x$.

A graph passes through $(5, 15)$. $k = 15 \div 5 = 3$. Equation: $y = 3x$.

Skill 6: Compare Two Proportional Relationships

This is a common extended-response question. You might get two representations — a table and a graph, or two tables — and need to say which has a larger $k$.

Method: Find $k$ for each. Larger $k$ = steeper line = faster rate.

Table A: $k = 3$. Graph B: $k = 5$. Graph B has a larger constant.

Skill 7: Word Problems

"A car travels 240 miles in 4 hours at a constant speed. Write an equation for the relationship."

$k = 240 \div 4 = 60$. Equation: $y = 60x$ where $y$ is miles and $x$ is hours.

Watch for: The units. If the problem uses different units, your $k$ needs to match.

Skill 8: Interpret $k$

"A bakery uses 2 cups of sugar for every 3 batches of cookies. What does $k$ represent?"

$k = \frac{2}{3}$ cups of sugar per batch. $k$ is the amount of sugar needed for 1 batch.

Practice Problems

1. Table: $(1, 4), (2, 8), (3, 12), (4, 16)$. Proportional? $k$? Equation?
2. Graph passes through $(6, 2)$. What is $k$? Equation?
3. $y = 0.5x$. Find $k$.
4. Which has a larger $k$: $y = 7x$ or a table with $(2, 10)$?
5. A printer prints 45 pages in 3 minutes. Write $y = kx$ equation.

Answers: 1. Yes, $k = 4$, $y = 4x$. 2. $k = \frac{1}{3}$, $y = \frac{1}{3}x$. 3. $k = 0.5$. 4. $k = 7$ vs $k = 5$, so $y = 7x$. 5. $k = 15$, $y = 15x$.

Related: Check any table with the table checker, test graphs with the graph checker, or solve equations with the proportion solver.