Question
Indigo's car used 4 gallons of gas to drive 180 miles. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
Answers
GPT-4o mini
To create a table of equivalent ratios for Indigo's car, we need to find other distances it could travel with different amounts of gas used. We're given that 4 gallons allows the car to travel 180 miles.
To find equivalent ratios, we can calculate the distance per gallon and then scale that up or down to create new ratio pairs.
1. Calculate the distance per gallon:
\[
\text{Distance per gallon} = \frac{180 \text{ miles}}{4 \text{ gallons}} = 45 \text{ miles per gallon}
\]
Now let's create a table with equivalent ratios of gallons of gas to the distance traveled.
| Gallons (g) | Distance (miles) |
|-------------|-------------------|
| 1 | 45 |
| 2 | 90 |
| 3 | 135 |
| 4 | 180 |
| 5 | 225 |
| 6 | 270 |
| 7 | 315 |
Next, we can plot these points on coordinate axes. Here’s a brief guideline on how to do that:
- The x-axis will represent the gallons of gas used.
- The y-axis will represent the distance traveled in miles.
Plot the following points based on the table above:
- (1, 45)
- (2, 90)
- (3, 135)
- (4, 180)
- (5, 225)
- (6, 270)
- (7, 315)
### Visualization
Since I can't create visual representations, you can plot these points on a graph using any graphing tool or on a piece of graph paper. Each point corresponds to the gallons used (x-coordinate) and the distance traveled (y-coordinate).
Plotting the points and drawing a line through them should yield a straight line, indicating a linear relationship between gallons of gas and miles traveled.
To find equivalent ratios, we can calculate the distance per gallon and then scale that up or down to create new ratio pairs.
1. Calculate the distance per gallon:
\[
\text{Distance per gallon} = \frac{180 \text{ miles}}{4 \text{ gallons}} = 45 \text{ miles per gallon}
\]
Now let's create a table with equivalent ratios of gallons of gas to the distance traveled.
| Gallons (g) | Distance (miles) |
|-------------|-------------------|
| 1 | 45 |
| 2 | 90 |
| 3 | 135 |
| 4 | 180 |
| 5 | 225 |
| 6 | 270 |
| 7 | 315 |
Next, we can plot these points on coordinate axes. Here’s a brief guideline on how to do that:
- The x-axis will represent the gallons of gas used.
- The y-axis will represent the distance traveled in miles.
Plot the following points based on the table above:
- (1, 45)
- (2, 90)
- (3, 135)
- (4, 180)
- (5, 225)
- (6, 270)
- (7, 315)
### Visualization
Since I can't create visual representations, you can plot these points on a graph using any graphing tool or on a piece of graph paper. Each point corresponds to the gallons used (x-coordinate) and the distance traveled (y-coordinate).
Plotting the points and drawing a line through them should yield a straight line, indicating a linear relationship between gallons of gas and miles traveled.