Question

What equation represents the graphed function

Answer 1

Answer: $y=\dfrac{-1}{3}x+3$

Step-by-step explanation:

The equation of ab line that passes through two points (a,b) and (c,d) is given by :-

$(y-b)=\dfrac{d-c}{b-a}(x-a)$

From the given picture , the line is passing through points (0,3) and (3,2).

Then, the equation of the line will be :-

$(y-3)=\dfrac{2-3}{3-0}(x-0)$

$\Rightarrow y-3=\dfrac{-1}{3}x$

$\Rightarrow y=\dfrac{-1}{3}x+3$

Hence, the required equation of the line that represents the graphed function : $y=\dfrac{-1}{3}x+3$

Answer 2

From the graph you can see easily that the y-intercept is (0,3).

The line passes thru the 2 given points (0,3) and (3,2).
                                                           2-3
Thus, the slope of this line is    m  = -------- = -1/3
                                                           3- 0

and so the equation of the graphed line is    y = (-1/3)x + 3.