7th Grade Proportional Relationships and y = kx Lesson (Free PDF)
This grade 7 proportional relationships lesson for 7th Grade covers proportional relationships and y = kx (Common Core 7.RP.A.2), with a free PDF to print.
Two quantities are proportional when the ratio of one to the other is always the same. That constant ratio is the constant of proportionality k, and the relationship is written \(y = kx\). On a graph, a proportional relationship is a straight line through the origin, and the point \((1, k)\) shows the unit rate.
Grade 7 · Common Core State Standards: 7.RP.A.2
Key facts in this grade 7 proportional relationships lesson
- Proportional means \(y/x\) is the same number k for every pair.
- The equation of a proportional relationship is \(y = kx\).
- The graph is a straight line through the origin \((0, 0)\).
- The point \((1, k)\) on the graph gives the unit rate.
- A line that misses the origin, or a table with changing ratios, is not proportional.
What does it mean for two quantities to be proportional?
Two quantities are proportional when their ratio is always the same. If you buy twice as many pounds of apples, you pay twice as much.
In the table above, \(2.50 \div 1 = 2.50\), \(5.00 \div 2 = 2.50\), and so on, so \(k = 2.50\) dollars per pound.
How can you tell from a graph?
A graph shows a proportional relationship only when both of these are true: the points lie on a straight line, and the line passes through the origin \((0, 0)\).
The point \((1, k)\) always lies on the graph. Its y-coordinate is the unit rate. Here the line passes through \((1, 2)\), so \(k = 2\).
How do you write the equation y = kx?
Divide any y-value by its x-value to find k, then write \(y = kx\). Check one more pair to be safe.
- Choose a pair from the table, such as \((3, 7.50)\).
- Find \(k = 7.50 \div 3 = 2.50\).
- Write \(y = 2.5x\).
- Use it: for 6 pounds, \(y = 2.5 \times 6 = 15\) dollars.
What does a point on the graph mean?
A point \((x, y)\) tells a real pair of values. The point \((0, 0)\) means zero pounds cost zero dollars. The point \((1, 2.50)\) means 1 pound costs \(\$2.50\), which is the unit rate.
| Test | Proportional? |
|---|---|
| Constant ratio y/x in every pair | Yes |
| Straight line through (0, 0) | Yes |
| Line misses the origin | No |
| Ratios change from pair to pair | No |
Grade 7 proportional relationships lesson: questions and answers
How do you know if a table is proportional?
Divide y by x in every column. If all the quotients are equal, the relationship is proportional. If even one quotient is different, it is not.
What is the constant of proportionality?
It is the number k in \(y = kx\). It equals \(y/x\) for any pair and is the same as the unit rate.
Why must the graph pass through the origin?
In \(y = kx\), an x-value of 0 gives \(y = 0\). So the point \((0, 0)\) is always on the graph of a proportional relationship.
What does the point (1, r) mean on a graph?
The y-coordinate r is the amount that goes with 1 unit. In a proportional graph, r equals k, the unit rate.
Is every straight line proportional?
No. A straight line is proportional only if it passes through the origin. The line \(y = 2x + 3\) is straight but not proportional.
How to use this grade 7 proportional relationships lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the grade 7 proportional relationships lesson as a PDF with the button below and keep it with your notes.
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