In the given graph, lets mark two points:
Let [tex]A = (0,-3)[/tex] and [tex]B = (4,-2)[/tex]
The slope of the line is given by:
[tex]m = \frac{(-2)-(-3)}{(4)-(0)}[/tex]
[tex]m = \frac{-2+3}{4}[/tex]
[tex]m = \frac{1}{4}[/tex]
The equation of the line is given by:
[tex](y-y_1)=m(x-x_1)[/tex]
[tex](y-(-3))=(\frac{1}{4})(x-0)[/tex]
[tex]4(y+3)=x[/tex]
[tex]4y+12=x[/tex]
[tex]4y=x-12[/tex]
[tex]y= \frac{1}{4}x-3[/tex]
Therefore, the function equation represented by the graph is: [tex]f(x)= \frac{1}{4}x-3[/tex]
