Answer:
Part 1) The rate of change is 2
Part 2) The initial value is 3
Step-by-step explanation:
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate of the linear equation
b is the y-intercept
Remember that in a linear equation the rate of change is a constant and is equal to the slope and the initial value is equal to the y-intercept (value of y when the value of x is equal to zero)
step 1
Find the slope
we have the coordinates
A(0,3) and B(2,7)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute in the formula
[tex]m=\frac{7-3}{2-0}[/tex]
[tex]m=\frac{4}{2}=2[/tex]
therefore
The rate of change is 2
step 2
Find the y-intercept or initial value
Remember that the y-intercept is the value of y when the value of x is equal to zero
In this problem the y-intercept is given
The y-intercept is the point A(0,3)
so
[tex]b=3[/tex]
therefore
The initial value is 3
