A babysitting service charges an initial $5.00 fee plus an additional fee of $6.50 per hour. Write a linear equation in the form y=mx+b that represents this relationship where m is the slope and b is the y-intercept.
The linear equation that represents this relationship is:
y = 6.50x + 5.00
Where:
y is the total cost of the babysitting service
x is the number of hours the service is used
6.50 is the hourly rate charged by the service
5.00 is the initial fee charged by the service
The slope of the line is 6.50, which represents the hourly rate charged by the service. The y-intercept of the line is 5.00, which represents the initial fee charged by the service.
Well, here's a joke for you while we work on the problem:
Why couldn't the bicycle stand up by itself?
Because it was two-tired! 😄
Now, let's get back to the question. We can represent the charges using the linear equation y = mx + b, where y is the total cost, x is the number of hours, m is the rate per hour, and b is the initial fee.
In this case, the initial fee is $5.00, so b = $5.00. The additional fee per hour is $6.50, so m = $6.50.
Therefore, the linear equation would be y = 6.50x + 5.00.
And remember, if you need any more math or jokes, I'm here for you!
To write the linear equation that represents the relationship between the babysitting fee and the number of hours, we can use the slope-intercept form:
y = mx + b
In this case, y represents the total fee, x represents the number of hours, m represents the rate per hour, and b represents the initial fee.
The initial fee is $5.00, so the y-intercept is 5.
The additional fee per hour is $6.50, so the slope (m) is 6.50.
Putting it all together, the linear equation is:
y = 6.50x + 5.00
To write a linear equation in the form y=mx+b that represents the relationship between the total cost (y) and the number of hours (x) for the babysitting service, we need to determine the values of the slope (m) and the y-intercept (b).
Given that the babysitting service charges an initial fee of $5.00 plus an additional fee of $6.50 per hour, we can observe the following:
- The initial fee of $5.00 is constant, regardless of the number of hours.
- The additional fee per hour is a constant $6.50.
From this information, we can conclude that the slope represents the additional fee per hour, which is $6.50, and the y-intercept represents the initial fee, which is $5.00.
Therefore, the linear equation representing this relationship is:
y = 6.50x + 5.00
In this equation:
- y represents the total cost,
- x represents the number of hours,
- 6.50 represents the slope (additional fee per hour),
- 5.00 represents the y-intercept (initial fee).