Question

Write the equation of the line that passes through the points (3, 6) and (5, 18) using function notation.

Answer 1

The answer would be B: F(x) = 6x - 12

This line passes through both given points.

Answer 2

First, we must find the slope using the equation

$\frac{y_{2}-y_{1} } {x_{2}-x_{1}}$

We can substitute in our points and will get

$\frac{18-6}{5-3} =\frac{12}{2} = 6$

This means that our slope is m=6.

We can now use the point slope form to find the equation of the line. The equation for this is $y-y_{1} =m(x-x_{1})$

Now we can substitute in one of our point, (3,6) in this case.

$y-6 = 6(x-3)$

this simplifies to

$y= 6x-12$

now we can swap y for f(x) to put it in function notation

this means that the answer is $f(x) = 6x-12$; which means that the answer is b