Answer:
The rate of change is -5
The initial value is 25
Step-by-step explanation:
Since, this is a linear relation
so, we can select any two points and find equation of line
points are (1,20) and (3,10)
so,
[tex]x_1=1,y_1=20[/tex]
[tex]x_2=3,y_2=10[/tex]
now, we can find slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
now, we can plug values
[tex]m=\frac{10-20}{3-1}[/tex]
[tex]m=-5[/tex]
now, we can use point slope form of line
[tex]y-y_1=m(x-x_1)[/tex]
now, we can plug values
[tex]y-20=-5(x-1)[/tex]
now, we can solve for y
[tex]y=-5x+25[/tex]
we know that
slope is the rate of change
So, the rate of change is -5
For finding initial value , we can plug x=0 and find y
[tex]y=-5\times 0+25[/tex]
[tex]y=25[/tex]
So, initial value is 25
