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

ANSWER

f(x) = 3x - 6

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:

$m=\frac{y_1-y_2}{x_1-x_2}$

So the slope for this line is:

$m=\frac{0-6}{2-4}=\frac{-6}{-2}=3$

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:

$f(x)=3x-6$