Answer:
Part 1) The rate of change of the linear function is [tex]\frac{1}{3}[/tex]
Part 2) The initial value is -4
Step-by-step explanation:
Part 1) Find the rate of change
we know that
The rate of change of the linear function is the same that the slope of the linear function
To determine the slope we need two points
Looking at the graph
take the points (0,-4) and (3,-3)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{-3+4}{3-0}[/tex]
[tex]m=\frac{1}{3}[/tex]
therefore
The rate of change of the linear function is [tex]\frac{1}{3}[/tex]
Part 2) Find the initial value
we know that
The initial value or y-intercept is the value of y when the value of x is equal to zero
Looking at the graph
when the value of x is equal to zero
The value of y is equal to -4
so
The y-intercept is the point (0,-4)
therefore
The initial value is -4
