A store charges 16 dollars for every 2 notebooks. Let x = notebooks and y = dollars. Write the proportional equation y = kx.
k = ______ y = ______x
CCSS 7.RP.A.2b–c · verbal to equation
Write Proportional Equations from Verbal Descriptions
Move from a real situation to an equation instead of giving students a table first. Some prompts state the per-one rate directly; others give a scaled pair so students must find k before writing y = kx.
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Verbal Situations to y = kx
Verbal situation → y = kx · Grade 7 standard · Seed 261601
1.
2.
A printer produces 24 pages for every 3 minutes. Let x = minutes and y = pages. Write the proportional equation y = kx.
k = ______ y = ______x
3.
A store charges 14 dollars for every 2 notebooks. Let x = notebooks and y = dollars. Write the proportional equation y = kx.
k = ______ y = ______x
4.
A recipe uses 24 cups for every 4 batches. Let x = batches and y = cups. Write the proportional equation y = kx.
k = ______ y = ______x
5.
A store charges 6 dollars for every 1 notebook. Let x = notebooks and y = dollars. Write the proportional equation y = kx.
k = ______ y = ______x
6.
A cyclist travels 12 miles for every 4 hours. Let x = hours and y = miles. Write the proportional equation y = kx.
k = ______ y = ______x
7.
A store charges 5 dollars for every 1 notebook. Let x = notebooks and y = dollars. Write the proportional equation y = kx.
k = ______ y = ______x
8.
A printer produces 16 pages for every 2 minutes. Let x = minutes and y = pages. Write the proportional equation y = kx.
k = ______ y = ______x
9.
A cyclist travels 3 miles for every 1 hour. Let x = hours and y = miles. Write the proportional equation y = kx.
k = ______ y = ______x
10.
A printer produces 18 pages for every 3 minutes. Let x = minutes and y = pages. Write the proportional equation y = kx.
k = ______ y = ______x
Exact-construction rule: fraction unit rates stay rational, graph coordinates come from known equations, and money applications use integer cents. No answer key depends on a hidden rounding convention.
Writing y = kx from a description
When one quantity is a constant multiple of another, the relationship is proportional and can be written y = kx, where k is the amount per one unit. Find k in the sentence (the 'per' amount), choose letters for the two quantities, and write the equation. A fixed starting fee makes it a different kind of relationship.
Worked examples
- Each ticket costs $4. With t tickets, the cost is c = 4t.
- A car travels at 55 miles per hour. After t hours the distance is d = 55t.
- Apples cost $2.50 per pound, so the cost of p pounds is c = 2.50p.
- Not proportional: a $5 fee plus $3 per ride is c = 5 + 3r, which has an added constant.
Common slips
- Swapping the letters, so the multiplier ends up on the wrong quantity. The cost is 4 times the number of tickets, not the other way.
- Adding a constant when there is none. A proportional equation has no added number.
- Using the total instead of the unit rate for k.
How to use this worksheet
Ask students to underline the 'per' amount and to name what each letter stands for. The answer key gives the equation in the form y = kx.
Common Core connection
- 7.RP.A.2.c · Represent proportional relationships with equations and connect each variable to its meaning.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Note 1
Define what x and y mean before writing the equation.
Note 2
If the prompt gives several units at once, divide y by x to find the per-one constant k.
Note 3
Example: 'a car travels 24 miles in 3 hours at a steady speed' gives k = 24 divided by 3 = 8, so y = 8x.
Note 4
Check the equation by substituting the quantities from the verbal description.
Continue the 7.RP progression
Move to another Grade 7 representation or application
Quick answers
Are all prompts price problems?
No. The set mixes distance, recipes, pay, purchases, and production-rate contexts.
Can a student solve by copying the visible rate?
Not always. Standard and challenge modes sometimes give a scaled pair, such as 24 miles in 3 hours, so k must be computed first.
What if the sentence already states the rate?
Then k is given directly. '$3 per pound' means y = 3x with no calculation; only compute k when the prompt gives a scaled pair instead of a per-one amount.