Math Problem Statement
Two friends, Paisley and Omar, had just bought their first cars. The equation y, equals, 29, point, 5, xy=29.5x represents the number of miles, yy, that Omar can drive his car for every xx gallons of gas. The graph below represents the number of miles, yy, that Paisley can drive her car for every xx gallons of gas.
Solution
To analyze the situation:
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Omar's Efficiency: The equation indicates that Omar's car achieves a constant mileage of 29.5 miles per gallon.
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Paisley's Efficiency: Since her mileage is represented by a graph, we need to evaluate the graph to determine her car's efficiency, specifically the slope of the line if it is linear. The slope of the line in a distance-gas graph represents the miles per gallon (mpg).
Questions to clarify:
- Does Paisley's graph depict a straight line?
- If it's a straight line, what are two distinct points on the graph?
- If the graph isn't linear, how does the curve behave?
Please provide more information, like the graph or details about it, so I can help you compare the efficiencies of the two cars and answer further questions.
Would you like me to guide you on how to determine the slope or interpret the graph?
Related Questions:
- What does the slope of a line represent in real-world problems like this?
- How can you tell if a car is more efficient based on its graph?
- What is the equation of a line given two points from a graph?
- How does a linear relationship differ from a non-linear one in terms of gas mileage?
- Why is it useful to have a graph and an equation for such comparisons?
Tip:
Always check the units when working with equations and graphs—they ensure your interpretations are accurate!
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Unit Rates
Graph Interpretation
Formulas
y = mx + b (Slope-Intercept Form)
Slope = (y2 - y1) / (x2 - x1)
Theorems
Linear Relationship and Proportionality
Suitable Grade Level
Grades 8-10