Find the Constant

This worksheet asks students to find the constant of proportionality, k, when a relationship is proportional, or write NP when it is not. The problems use several formats, including equations, tables, ordered pairs, and real-world situations. That means students must first decide whether the relationship is proportional and then, if it is, identify the value of k that connects x and y.

For a parent, the constant of proportionality is simply the number that tells how much y changes for each 1 unit of x. In a proportional relationship, y = kx. So if y = 6x, then k = 6. If a table shows y/x = 5 for every pair, then k = 5. If the relationship has a starting fee or the ratios are inconsistent, there is no single k, so students write NP.

Learning Goals

• Identify k from Equations: Students read the coefficient in y = kx.
• Find k from Tables and Ordered Pairs: Learners calculate y/x.
• Interpret k in Real Situations: Students connect the constant to a rate, such as dollars per item.
• Recognize Non-Proportional Cases: Learners write NP when no constant ratio exists.
• Connect Representations: Students see that the same constant can appear in equations, tables, and word problems.

Parent-Friendly Teaching Tips

For each problem, ask:

“Is there one number that always multiplies x to give y?”

If yes, that number is k.

Examples:

y = 6x

k = 6

Table:

x: 2, 4, 6, 8
y: 5, 10, 15, 20

5 ÷ 2 = 2.5
10 ÷ 4 = 2.5
15 ÷ 6 = 2.5
20 ÷ 8 = 2.5

So k = 2.5.

But if a situation says there is a $5 sign-up fee plus $4 per month, the relationship is non-proportional, so write NP.

Why This Worksheet Helps

• Makes k More Concrete: Students see the constant across several formats.
• Builds Connection to Unit Rate: In many situations, k is the “per one” rate.
• Strengthens Algebra Readiness: Students understand the role of the coefficient in y = kx.
• Encourages Classification Before Calculation: Learners first decide whether a constant even exists.
• Supports Graphing: In proportional relationships, k also connects to the steepness of the line.

The real value of this worksheet is that it helps students understand the constant of proportionality as the one number that holds the whole relationship together. Equations, tables, ordered pairs, unit rates, and real-world situations all connect through k. For parents, the best reminder is: “If y is always the same multiple of x, that multiplier is k.”