8th Grade Proportional Relationships and Slope Lesson (Free PDF)
This grade 8 proportional relationships lesson for 8th Grade covers proportional relationships and slope (Common Core 8.EE.B.5), with a free PDF to print.
A proportional relationship has a constant ratio between two quantities, so it can be written y = kx. Its graph is a straight line through the origin. The constant k is the unit rate, and it equals the slope of the line, which is rise divided by run between any two points.
Grade 8 · Common Core State Standards: 8.EE.B.5
Key facts in this grade 8 proportional relationships lesson
- Equation: \(y = kx\), where \(k = \frac{y}{x}\) is the unit rate.
- The graph is a straight line through the origin \((0, 0)\).
- Slope = \(\frac{\text{rise}}{\text{run}}\), the same between any two points on the line.
- A greater unit rate means a steeper line.
- In a table, check that \(\frac{y}{x}\) is constant.
What is a proportional relationship?
Two quantities are in a proportional relationship when one is always a constant multiple of the other. That constant is the unit rate, written \(k\) in the equation \(y = kx\).
How does the graph show the unit rate?
Pick any point on the line and read its coordinates. For the line below, the point \((2, 6)\) shows 6 miles in 2 hours. The unit rate is the value at \(x = 1\), which is 3 miles per hour.
What is slope?
Slope measures how steep a line is. Move from one point to another: the vertical change is the rise and the horizontal change is the run. The slope is \(\frac{\text{rise}}{\text{run}}\), and for a proportional relationship it equals the unit rate.
Here the slope is \(\frac{6}{4} = \frac{3}{2}\), so \(y = \frac{3}{2}x\). A steeper line has a greater slope. A line that goes down from left to right has a negative slope.
How do you compare two proportional relationships?
Find the unit rate of each, then compare. Suppose Car A is shown by \(y = 55x\) and Car B travels 120 miles in 2 hours. Car B’s rate is \(120 \div 2 = 60\) miles per hour, which is faster than 55.
- Find the unit rate of each relationship (divide \(y\) by \(x\)).
- Check that each graph passes through the origin.
- Compare the unit rates: the greater rate is the steeper line.
Not proportional: the table \(x = 1, 2, 3\) with \(y = 5, 9, 13\) has \(\frac{y}{x}\) values 5, 4.5 and 4.33. They are not equal, and the line would not pass through the origin.
Grade 8 proportional relationships lesson: questions and answers
How can I tell if a table is proportional?
Divide each y by its x. If every quotient is the same number, the relationship is proportional. If they differ, it is not.
Why does a proportional graph go through the origin?
When \(x = 0\), \(y = k \cdot 0 = 0\). So the point \((0, 0)\) is always on the line.
Is slope the same as unit rate?
For a proportional relationship, yes. The unit rate is the y-value when \(x = 1\), which is also rise over run. In other lines, slope is a rate of change.
Can the slope be a fraction?
Yes. A line through \((0, 0)\) and \((4, 6)\) has slope \(\frac{6}{4} = \frac{3}{2}\). The unit rate is 1.5.
How do I compare a graph and an equation?
Read the unit rate from the graph at \(x = 1\) or by rise over run, and read \(k\) from the equation. Then compare the two numbers.
How to use this grade 8 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 8 proportional relationships lesson as a PDF with the button below and keep it with your notes.
All Grade 8 chapters: Grade 8 math.
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