Suppose you are saving money for a new cell phone. At week 0 you have $20 and at week 10 you have $100. If y represents the amount of money you have saved and x represents the number of weeks, find and interpret the slope of the linear equation
To find the slope of the linear equation, we need to use the formula for calculating slope, which is:
slope (m) = (change in y) / (change in x)
In this case, the change in y represents the change in the amount of money saved, and the change in x represents the change in the number of weeks.
Using the given information, we can calculate the change in y and x:
Change in y = $100 - $20 = $80
Change in x = 10 weeks - 0 weeks = 10 weeks
Now, we can substitute these values into the slope formula:
slope (m) = (change in y) / (change in x)
= $80 / 10 weeks
= $8 per week
Interpretation:
The slope of the linear equation is $8 per week. This means that for each week that passes, the amount of money you save increases by $8.
To find the slope of the linear equation, we can use the formula:
slope (m) = (change in y)/(change in x)
In this case, the change in y is the difference between the amount of money saved at week 10 ($100) and week 0 ($20), which is:
change in y = $100 - $20 = $80
The change in x is the difference between week 10 and week 0, which is:
change in x = 10 weeks - 0 weeks = 10 weeks
Using the formula, the slope is:
slope (m) = (change in y)/(change in x) = $80/10 weeks = $8/week
Interpreting the slope: The slope of $8/week means that, on average, you are saving $8 per week towards your new cell phone.
To find the slope of the linear equation, we can use the formula:
slope = change in y / change in x
In this case, the change in y represents the change in the amount of money saved, and the change in x represents the change in the number of weeks.
Given that at week 0, you have $20, and at week 10, you have $100, we can calculate the changes as:
change in y = $100 - $20 = $80
change in x = 10 - 0 = 10
Now, we can compute the slope:
slope = change in y / change in x = $80 / 10 = $8
Interpreting the slope:
The slope of $8 tells us that, on average, you are saving $8 per week towards your new cell phone. This means that for every additional week, you can expect your savings to increase by $8.
Therefore, the slope of the linear equation represents the rate of change in savings per week.