To answer the questions, we need to establish a linear equation in slope-intercept form. While you have not provided a specific equation, I'll assume a typical format for a bike rental cost example. Let's say the equation is:
\[ y = mx + b \]
where \( y \) represents the total cost of renting the bike, \( x \) represents the number of hours rented, \( m \) is the slope (cost per hour), and \( b \) is the y-intercept (fixed cost or starting cost).
Let’s use an example with a slope of 20 and a y-intercept of 0. Thus, the equation would be:
\[ y = 20x \]
Using this equation, we can answer each question:
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The linear equation written in slope-intercept form is: \[ y = 20x \]
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The cost of renting the bike for 2 hours is: \[ y = 20(2) = 40 \] So, it costs $40 to rent the bike for 2 hours.
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(4, _) is on the linear equation: To find the y-coordinate when \( x = 4 \): \[ y = 20(4) = 80 \] Thus, the point is \( (4, 80) \).
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The point (6,50) represents that it costs $: To find out if this point is on our line - the cost for 6 hours would be: \[ y = 20(6) = 120 \] So, \( (6, 50) \) does not fit our equation with \( y = 120 \) for 6 hours; thus it likely represents an incorrect interpretation or slope. But based on this equation, it represents:
- It cost $50 to rent the bike for 2.5 hours (because \( 50 = 20x \Rightarrow x = 2.5 \)).
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The y-intercept is located at: Since there is no fixed cost in our equation, the y-intercept is: \[ (0, 0) \]
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The y-intercept represents that at 0 hour(s), the cost of the bike rental is: At \( 0 \) hours, the cost is $0.
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For $60, you can rent the bike for: To find out how many hours this cost represents: \[ 60 = 20x \Rightarrow x = 3 \] Thus, for $60, you can rent the bike for 3 hours.
Please adjust any example numbers based on the actual values or slopes relevant to your specific problem if those differ!