Question

30 POINTS By looking at the intercepts, which linear function does the graph represent?

A. f(x)=2/3x+2
B. f(x)=2/3x+3
C. f(x)=2/3x-2

Answer 1

C. f(x)=2/3x-2

Explanation:

Looking at the graph we realize that the y-intercept is given by:

$b=-2$

The Slope-intercept form of the equation of a line is given by:

$y=mx+b$

So, our equation becomes:

$y=mx-2$

So the only option that matches a negative y-intercept is C. Let's see that the slope $m=2/3$. Look at the y-intercept, if you increase x by 3 units, then y increases by 2 units and goes from $x=-2$ to $x=0$. In other words:

$Change \ in \ x=\Delta x=3 \\ \\ Change \ in \ y=\Delta y=2 \\ \\ \\ m=\frac{\Delta y}{\Delta x}=\frac{2}{3}$

Learn more:

Writing linear equations: https://brainly.com/question/12169569

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