Math Problem Statement
Solution
To solve this, we’ll examine the graph and address each question.
Observations from the Graph
The graph shows a linear relationship between the distance traveled (in miles) on the x-axis and the number of gallons used on the y-axis.
- At approximately 100 miles, the train has used 100 gallons.
- At approximately 400 miles, the train has used 400 gallons.
Since this is a direct variation, we can calculate the fuel usage rate and the slope.
Solution for Part (a): Gallons Used per Mile
The gallons per mile is determined by the ratio of gallons to miles. Here’s how we can find it:
So, the train uses 1 gallon per mile.
Solution for Part (b): Slope of the Graph
The slope of a line in a graph showing direct variation is equivalent to the rate calculated above, as the slope represents "gallons per mile."
Therefore, the slope is also 1.
Summary of Answers
- (a) The train uses 1 gallon per mile.
- (b) The slope of the graph is 1.
Would you like further details on this solution or have any questions?
Related Questions
- How would the slope change if the train used more gallons per mile?
- What would the graph look like if the fuel usage rate was 0.5 gallons per mile?
- How can we interpret the y-intercept in the context of this problem?
- What does it mean if the slope were greater than 1?
- How would the graph change if the train carried more weight?
Tip:
In direct variation problems, identifying two clear points can simplify finding the rate or slope.
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Math Problem Analysis
Mathematical Concepts
Direct Variation
Linear Functions
Slope Calculation
Formulas
Slope formula: (y2 - y1) / (x2 - x1)
Direct Variation formula: y = kx
Theorems
Direct Variation
Suitable Grade Level
Grades 6-8