Given:
The function that represents how the amount of fuel changes as a function of distance flown is
where x represents miles flown, and f(x) represents the amount of fuel remaining.
To find:
The rate of change for this scenario.
Solution:
The slope intercept form of a linear function is
...(i)
Where, m is the slope or rate of change and b is the y-intercept.
We have,
...(ii)
On comparing (i) and (ii), we get
Therefore, the rate of change for this scenario is -0.9. It means, the amount of fuel in the airplane is decreasing by 0.9 gallons per mile.
Symbolab has a calculator that solves problems like that and works it out for you, to help understand it better :)
Put the equation in Slope Intercept Form. Then graph the y-intercept point. From the y intercept point use the slope to find your second point. Finally, draw the line using those points.
Okay. Let us do it surgically. Let us solve first the rate of increase in Lliana's Math grade. 86-65 = 21, thus the rate can be written as a fraction 21/65. We will reserve the decimal form once we are done with both rates of increase.
On the same note, Fiona's increase in Math grade is determined by subtracting 70 from her recent grade of 80, thus giving us an increase in her grade by 10. Therefore, the rate of increase in her Math grade is 10/70.
Now, let us take the decimal forms of the students' grade in math respectively. Lliana's is 21/65 or 0.32307692307... Fiona's is 10/70 or 0.14285714285. Now, subtracting this decimals we have 0.18021978021.
Changing it to percent form, we must multiply it by 100 and add the symbol "%". Therefore, we have 18.021978021 %.
Finally, rounding the value to the nearest whole number, we obtained 18.00% or just 18%.
