1. 3.4
Direct Variation
How can you solve problems involving direct variation?

2. Texas Essential Knowledge and Skills
The student is expected to:
Proportionality—8.5.E
Solve problems involving direct variation.
Mathematical Processes
8.1.B
Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

3. ADDITIONAL EXAMPLE 1
The time it takes to hear thunder varies directly with the distance from a lightning bolt.
Determine whether the data set shows direct variation. If so, write an equation that describes the relationship.
The data set shows direct variation. The equation is y = 0.2x.

4. ADDITIONAL EXAMPLE 2
The speed limit in Mexico and Canada is in kilometers per hour. Speed in miles per hour varies directly as speed in kilometers per hour. What is the approximate speed limit in mi/h if a sign shows a speed limit of 110 km/h?
y x; about 68 mi/h

5. 3.4 LESSON QUIZ
8.5.E 1.
Weight on Mars varies directly with weight on Earth as shown in this table. Write an equation that describes the relationship.
y = 0.377x

6. 2.
The cost of buying bags of apples for the Harvest Festival varies directly with the number of bags purchased. What will be the cost of purchasing 7 bags?
$35

7. 3.
The table shows how the perimeter of a regular pentagon changes as side length increases. Does the perimeter vary directly with the side length? If so, write an equation that describes the relationship.
Yes; y = 5x 4.
Does the equation y = 1.06x + 3 show a direct variation? Explain.
No; the graph of this equation does not pass through the origin.

8. Have students explore a negative value for k by looking at a relationship such as the one in this table.
In a direct variation, the ratio between the variables stays constant. Does the ratio between y and x remain constant for this table? Explain.

9. Have students explore a negative value for k by looking at a relationship such as the one in this table.
In the equation for this relationship, y = kx, what is the value of k?
–1.5
Write the equation.
y = –1.5x
In which quadrant will the graph of this equation be? IV

10. How can you solve problems involving direct variation?
Sample answer:
Use ratios of values from a table or a graph of a line to find the equation. Then substitute to make predictions.