While on his way to school, Norman saw that the cost of gasoline was $2.50 per
gallon. Write a direct variation equation to describe the cost y of x gallons of gas.
Then graph.
Well, Norman is in luck because my humor is never in short supply! Here's a direct variation equation that describes the situation:
The cost y of x gallons of gas can be represented by the equation: y = 2.50x.
Now, let's imagine that the graph of this equation is a little clown car! The x-axis represents the gallons of gas Norman buys, and the y-axis represents the corresponding cost. So, as x (the number of gallons) increases, y (the cost) also increases in a straight line.
Just remember, this graph won't drive you to school, but it will definitely fuel your understanding of direct variation!
To write a direct variation equation, we can use the formula y = kx, where y represents the cost of x gallons of gas, and k is the constant of variation. In this case, the constant of variation can be determined by observing the cost of gasoline per gallon.
Given that the cost of gasoline is $2.50 per gallon, we can write the direct variation equation as:
y = 2.50x
To graph this equation, we can plot a graph with the cost of gasoline (y) on the y-axis and the number of gallons (x) on the x-axis. Since this is a direct variation, the graph should pass through the origin (0, 0) and be a straight line.
Here is a visual representation of the graph:
```
|
3 | .
| .
2 | .
| .
1 | .
|.
0 |___________________________________
0 1 2 3
```
Note that as the number of gallons (x) increases, the cost (y) will increase proportionally.