Sangeetha Pulapaka

The function notation to describe the points given, will be f(0) = 3 and f(4) = 6.

This is because a function notation is of the form y = f(x), where x is the input of the function and y is the output.

So when x = 0, y = 3, and when x = 4, y = 6.

Read on if you want to know how to find the equation of the line which runs through the points (0,3) and (4,6)

The equation of the line as you may recall is, in the form y = mx+ c where m is the slope and c is the y-intercept.

We use the slope formula between the two points (0,3) (4,6) to find out the slope of the line, m,

m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{6-3}{4-0} = \frac{3}{4}

Plug in one of the points in the equation to find the y-intercept.

Plug in (0,3) and   m = \frac{3}{4} in y = mx+ c.

to get 3 = \frac{3}{4} \cdot 0 + c

\Rightarrow c = 3

So, the equation of the line is y = \frac{3}{4} x + 3


When x = 0, f(3) = \frac{3}{4} \cdot 0 + 3 = 3

When x = 4, f(4) = \frac{3}{4} \cdot 4 + 3 = 6

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