Question

find an equation of the line passing through the given points use function notation to write the equation (2, 0) and (4, 6)

Answer 1

f(x) = 3x - 6

Step-by-step explanation

The equation of a line is:

`f(x)=mx+b`

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

The formula for the slope of a line passing through points (x1, y1) and (x2, y2) is:

`m=(y_1-y_2)/(x_1-x_2)`

So the slope for this line is:

`m=(0-6)/(2-4)=(-6)/(-2)=3`

For now we have :

`f(x)=3x+b`

To find the y-intercept b we have to replace with one of the points and solve for b:

`\begin{gathered} f(2)=0=3\cdot2+b \\ 0=6+b \\ b=-6 \end{gathered}`

So the equation is:

`f(x)=3x-6`