Question

Which equation represents the graph function?

Answer 1

`\displaystyle y=-(1)/(3)x+3`

Explanation:

First, notice that since the graph of the function is a line, we have a linear function.

To find the equations for linear functions, we need the slope and the y-intercept. Recall the slope-intercept form:

`y=mx+b`

Where m is the slope and b is the y-intercept.

We are given the point (0,3) which is the y-intercept. Thus, b = 3.

To find the slope, we can use the slope formula:

`\displaystyle m=(\Delta y)/(\Delta x) =(2-3)/(3-0)=-1/3`

Therefore, our equation is:

`\displaystyle y=-(1)/(3)x+3`