Answer:
[tex]f(x)=-\frac{1}{2}x+2[/tex]
Step-by-step explanation:
We have been given a graph of a function and we are asked to find the equation for our given function.
We will write formula for our given function in slope-intercept form of equation: [tex]y=mx+b[/tex], where,
m = Slope of line,
b = The y-intercept or initial value.
Let us find slope of our given line using slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where,
[tex]y_2-y_1[/tex] = Difference between two y-coordinates,
[tex]x_2-x_1[/tex] = Difference between two x-coordinates of same y-coordinates.
Upon substituting coordinates of points (0,1) and (2,0) in slope formula we will get,
[tex]m=\frac{0-1}{2-0}[/tex]
[tex]m=\frac{-1}{2}[/tex]
[tex]m=-\frac{1}{2}[/tex]
We can see that initial value of our function is 2, so y-intercept will be 2.
Upon substituting our given values in slope-intercept form of equation we will get our function formula as:
[tex]f(x)=-\frac{1}{2}x+2[/tex]
Therefore, the equation [tex]f(x)=-\frac{1}{2}x+2[/tex] is represented by our given function.
