Question

What function equation is represented by the graph?

Answer 1

In the given graph, lets mark two points:

Let $A = (0,-3)$ and $B = (4,-2)$

The slope of the line is given by:

$m = \frac{(-2)-(-3)}{(4)-(0)}$

$m = \frac{-2+3}{4}$

$m = \frac{1}{4}$

The equation of the line is given by:

$(y-y_1)=m(x-x_1)$

$(y-(-3))=(\frac{1}{4})(x-0)$

$4(y+3)=x$

$4y+12=x$

$4y=x-12$

$y= \frac{1}{4}x-3$

Therefore, the function equation represented by the graph is: $f(x)= \frac{1}{4}x-3$