Respuesta :
It is a question for linear equation
Let the number of donuts be y and the time be x
Since she can make 30 donuts from 8:15 to 9:00
We will find how many minutes from 8:15 to 9:00
There are 45 minutes from 8:15 to 9:00
Then the first point is (45, 30)
We need to find how many donuts she can make from 7:35 to 8:15
Since there are 25 minutes from 7:35 to 8:00
Since there are 15 minutes from 8:00 to 8:15, then
There are 25 + 15 = 40 minutes from 7:35 to 8:15
By using the proportional way we can find the number of donuts
[tex]\frac{30}{45}=\frac{x}{40}[/tex]By using the cross multiplication
[tex]\begin{gathered} x\times45=30\times40 \\ 45x=1200 \end{gathered}[/tex]Divide both sides by 45
[tex]\begin{gathered} \frac{45x}{45}=\frac{1200}{45} \\ x=26.66666 \end{gathered}[/tex]Then she can finish 26 donuts before 8:15
b.
The form of the slope-intercept form is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept (initial amount)
Since she will start counting from 8:15
Then the initial amount will be the 26 donuts
b = 26
The slope will be the ratio between the number of donuts and the time
[tex]\begin{gathered} m=\frac{30}{45} \\ m=\frac{2}{3} \end{gathered}[/tex]The equation is
[tex]y=\frac{2}{3}x+26[/tex]