What does the graph represent in terms of gallons of gasoline used and miles traveled?
Understand the Problem
The question is asking about the relationship between the gallons of gasoline used and the miles traveled, as represented by the graph. This involves understanding linear relationships and possibly calculating mileage or slope.
Answer
The equation relating gallons of gasoline used to miles traveled is \( y = 20x \).
Answer for screen readers
The linear equation is given by ( y = 20x ), where ( y ) represents miles traveled and ( x ) represents gallons of gasoline used.
Steps to Solve
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Identify Key Points First, identify two points on the line from the graph. For example, from the graph, we can select the points (2, 40) and (4, 80).
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Calculate the Slope The slope ($m$) of the line can be calculated using the formula: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ Substituting our identified points, we have: $$ m = \frac{80 - 40}{4 - 2} = \frac{40}{2} = 20 $$
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Write the Equation of the Line Using the slope-point form of the line, we use one point, say (2, 40): $$ y - y_1 = m(x - x_1) $$ So, substituting we get: $$ y - 40 = 20(x - 2) $$
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Rearrange to Slope-Intercept Form Distributing and rearranging gives us: $$ y - 40 = 20x - 40 $$ Thus: $$ y = 20x $$
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Interpret the Equation This equation shows the direct relationship between gallons of gasoline used ($x$) and miles traveled ($y$), indicating that for every gallon used, 20 miles are traveled.
The linear equation is given by ( y = 20x ), where ( y ) represents miles traveled and ( x ) represents gallons of gasoline used.
More Information
The slope of the equation indicates that for every gallon of gasoline consumed, 20 miles are traveled. This demonstrates a clear linear relationship between the two variables.
Tips
- Misidentifying Points: Ensure that you accurately read and select points from the graph.
- Forgetting to Simplify: When calculating the slope or rearranging equations, remember to simplify fully.
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