To determine which graph represents the equation \( y = -\frac{1}{20}x + 10 \), let's break down the equation:
- The y-intercept is \( 10 \), which means when \( x = 0 \) (when no miles have been driven), the gasoline remaining in the car is \( 10 \) gallons.
- The slope of the line is \( -\frac{1}{20} \), which means for every \( 20 \) miles driven, \( 1 \) gallon of gasoline is used.
Now, we can analyze the options given:
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First option: Line goes through points \( (0, 10) \) and \( (40, 8) \):
- From \( (0, 10) \) to \( (40, 8) \), the line decreases by \( 2 \) gallons when \( x \) increases from \( 0 \) to \( 40 \) miles.
- This means \( 40 \) miles corresponds to \( 2 \) gallons used. This checks out because \( \frac{40 \text{ miles}}{20} = 2 \) gallons, which aligns with the slope and \( y \)-intercept of the equation.
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Second option: Line goes through points \( (0, 11) \) and \( (80, 8) \):
- The line does not start at \( 10 \). It starts at \( 11 \) gallons, which is incorrect.
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Third option: Line goes through points \( (0, 12) \) and \( (125, 6) \):
- This also does not start at \( 10 \) gallons, but at \( 12 \), which is incorrect.
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Fourth option: Line goes through points \( (0, 10) \) and \( (150, 0) \):
- This starts at \( 10 \) gallons when \( x = 0 \), but it shows \( 150 \) miles corresponding to \( 0 \) gallons. This implies that with a linear decrease, it uses \( 10 \) gallons over \( 150 \) miles. However, that yields a slope of \( -\frac{10}{150} = -\frac{1}{15} \), which does not match our equation.
From this analysis, the correct option that matches the equation \( y = -\frac{1}{20}x + 10 \) is the first option: A graph that goes through points \( (0, 10) \) and \( (40, 8) \).
1 answer