Question

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

Answer 1

Answer:

$f(x) = 6x -12$

Step-by-step explanation:

We must write the function of the line in the form $f (x) = mx + b$

First calculate the slope m

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

$y_2 = 18\\y_1 =6\\x_2=5\\x_1=3$

$m= \frac{18-6}{5-3} = 6$

Then

$f(x) = 6x +b$

To have b replaced a point in the function

$f(3)=6 = 6(3) +b\\\\6-18= b\\\\b=-12$

Finally the function is

$f(x) = 6x -12$

Answer 2

ANSWER

$f(x) = 6x - 12$

EXPLANATION

The given line passes through the points (3, 6) and (5, 18).

The slope of this line given by:

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

We plug in the points to get,

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

The equation is given by

$y-y_1=m(x-x_1)$

We plug in the point and the slope to get,

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

$y - 6 = 6x - 18$

$y = 6x - 18 + 6$

$y = 6x - 12$

Using function notation, we have

$f(x) = 6x - 12$