Answer:
Part 1) The rate of change is [tex]\frac{1}{3}[/tex]
Part 2) The initial value is [tex]12[/tex]
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 rate of change
b is the y-intercept or initial value
step 1
Find the slope or rate of change
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the points
(3,13) and (6,14)
substitute the values in the formula
[tex]m=\frac{14-13}{6-3}[/tex]
[tex]m=\frac{1}{3}[/tex]
therefore
The rate of change is [tex]\frac{1}{3}[/tex]
step 2
Find the initial value
we have
[tex]m=\frac{1}{3}[/tex]
[tex]point\ (3,13)[/tex]
substitute in the equation [tex]y=mx+b[/tex]
[tex]13=\frac{1}{3}(3)+b[/tex]
solve for b
[tex]13=1+b[/tex]
[tex]b=13-1=12[/tex] ---> initial value
The linear equation is equal to
[tex]y=\frac{1}{3}x+12[/tex]
The y-intercept or initial value is 12
