Answer:
Initial value \(12\), rate of change: \(-2\)
Step-by-step explanation:
Step 1
Find the rate of change
we know that
In a linear equation the rate of change is equal to the slope
The formula to calculate the slope between two points is equal to
\(m=\frac{y2-y1}{x2-x1}\)
we have
\(A(1,10)\ B(2,8)\)
Substitute the values
\(m=\frac{8-10}{2-1}\)
\(m=-2\) ----> rate of change
Step 2
Find the initial value
The equation of the line into slope-point form is equal to
\(y-y1=m(x-x1)\)
Substitute
\(y-10=-2(x-1)\)
\(y=-2x+2+10\)\(y=-2x+12\)
The initial value is the value of y when the value of x is equal to zero (is the y-intercept)
\(y=-2*0+12=12\)----> initial value
