can u make this smaller
A. To find the rate of change and initial value for Sarah's business, we can use the given data from 2010 and 2014. The rate of change represents how much the fee increases each year, and the initial value represents the fee in the starting year.
From 2010 to 2014, the number of years that passed is 2014 - 2010 = 4 years.
The increase in the dog-walking fee is $750 - $350 = $400.
To find the rate of change, we divide the increase in the fee by the number of years: $400/4 years = $100/year.
Therefore, the rate of change for Sarah's business is $100 per year.
The initial value is the fee in the starting year, which is $350 in 2010.
Therefore, the initial value for Sarah's business is $350.
B. To write an equation in slope-intercept form to represent the fees that Sarah charges each year, we can use the rate of change and initial value we found.
The slope-intercept form of an equation is y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept (initial value).
For Sarah's business, the equation would be y = 100x + 350, where x represents the number of years since 2010 and y represents the dog-walking fee.
Therefore, the equation to represent the fees that Sarah charges each year is y = 100x + 350.
A. Find rate of change and initial value:
Rate of change: $100/year
Initial value: $350
B. Equation in slope-intercept form:
y = 100x + 350
and show the steps
A. To find the rate of change and initial value:
1. Calculate the number of years that passed from 2010 to 2014:
Number of years = 2014 - 2010 = 4 years.
2. Calculate the increase in the dog-walking fee by subtracting the fee in 2010 from the fee in 2014:
Increase in fee = $750 - $350 = $400.
3. Determine the rate of change by dividing the increase in the fee by the number of years:
Rate of change = Increase in fee / Number of years = $400 / 4 years = $100/year.
Therefore, the rate of change for Sarah's business is $100 per year.
4. To find the initial value, identify the fee in the starting year, which is $350 in 2010.
Therefore, the initial value for Sarah's business is $350.
B. To write an equation in slope-intercept form:
1. The slope-intercept form of an equation is y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept (initial value).
2. For Sarah's business, the equation becomes y = 100x + 350, where x represents the number of years since 2010 and y represents the dog-walking fee.
Therefore, the equation to represent the fees that Sarah charges each year is y = 100x + 350.