Question
The linear equation represented on the coordinate plane represents the cost of renting a bike per hour.
(1 point)
1) The liner equation written in slope-intercept form is
2) The cost of renting the bike for 2 hours is $
3) (4,
) is on the linear equation.
4) The point (6,50) represents that it cost $
to rent the bike for
hours
5) The y-intercept is located at
(write your answer as an ordered pair)
6) The y-intercept represents that at
hour(s), the cost of the bike rental is $
7) For $60, you can rent the bike for
hours
(1 point)
1) The liner equation written in slope-intercept form is
2) The cost of renting the bike for 2 hours is $
3) (4,
) is on the linear equation.
4) The point (6,50) represents that it cost $
to rent the bike for
hours
5) The y-intercept is located at
(write your answer as an ordered pair)
6) The y-intercept represents that at
hour(s), the cost of the bike rental is $
7) For $60, you can rent the bike for
hours
Answers
GPT-4o mini
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:
1) **The linear equation written in slope-intercept form is:**
\[ y = 20x \]
2) **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.
3) **(4, _) is on the linear equation:**
To find the y-coordinate when \( x = 4 \):
\[ y = 20(4) = 80 \]
Thus, the point is \( (4, 80) \).
4) **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 \( 50 = 20x \Rightarrow x = 2.5 \)).
5) **The y-intercept is located at:**
Since there is no fixed cost in our equation, the y-intercept is:
\[ (0, 0) \]
6) **The y-intercept represents that at 0 hour(s), the cost of the bike rental is:**
At \( 0 \) hours, the cost is **$0**.
7) **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!
\[ y = mx + b \]
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:
1) **The linear equation written in slope-intercept form is:**
\[ y = 20x \]
2) **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.
3) **(4, _) is on the linear equation:**
To find the y-coordinate when \( x = 4 \):
\[ y = 20(4) = 80 \]
Thus, the point is \( (4, 80) \).
4) **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 \( 50 = 20x \Rightarrow x = 2.5 \)).
5) **The y-intercept is located at:**
Since there is no fixed cost in our equation, the y-intercept is:
\[ (0, 0) \]
6) **The y-intercept represents that at 0 hour(s), the cost of the bike rental is:**
At \( 0 \) hours, the cost is **$0**.
7) **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!