Answer:
2
Step-by-step explanation:
Let's find the function first. We know that the function join the points (0, 2) and (5, 0) with a line, so we have a linear function. We need to find the slope of the line joining those two points using the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where
[tex]m[/tex] is the slope of the line
[tex](x_1, y_1)[/tex] are the coordinates of the first point
[tex](x_2,y_2)[/tex] are the coordinates of the second point
Our first point is (0, 2), so [tex]x_1=0[/tex] and [tex]y_1=2[/tex]; our second point is (5, 0), so [tex]x_2=5[/tex] and [tex]y_2=0[/tex]. Replacing the values:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{0-2}{5-0}[/tex]
[tex]m=\frac{-2}{5}[/tex]
[tex]m=-\frac{2}{5}[/tex]
Now that we have the slope of our line, we can use the point-slope formula to complete our function:
[tex]y-y_1=m(x-x_1)[/tex]
where
[tex]m[/tex] is the slope
[tex](x_1,y_1)[/tex] are the coordinates of the first point
Replacing values:
[tex]y-2=-\frac{2}{5}(x-0)[/tex]
[tex]y-2=-\frac{2}{5} x[/tex]
[tex]y=-\frac{2}{5} x+2[/tex]
[tex]f(x)=-\frac{2}{5} x+2[/tex]
Now, the initial value of our function is the value at [tex]x=0[/tex], so:
[tex]f(0)=-\frac{2}{5} (0)+2[/tex]
[tex]f(0)=2[/tex]
We can conclude that the initial value of the function is 2.
