# How do you write the equation of the line that passes through the points (3, 6) and (5, 18) using function notation?

Aug 8, 2018

$f \left(x\right) = 6 x - 12$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+c

$\text{where m is the slope and c the y-intercept}$

$\text{calculate m using the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(3,6)" and } \left({x}_{2} , {y}_{2}\right) = \left(5 , 18\right)$

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

$y = 6 x + c \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find c substitute either of the 2 given points into}$
$\text{the partial equation}$

$\text{using "(3,6)" then}$

$6 = 18 + c \Rightarrow c = 6 - 18 = - 12$

$y = 6 x - 12 \text{ or } f \left(x\right) = 6 x - 12$

Aug 8, 2018

$y = 6 x - 12$

#### Explanation:

After using formula equation of line passes through 2 points,

$\frac{y - 6}{x - 3} = \frac{18 - 6}{5 - 3}$

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

$y - 6 = 6 \cdot \left(x - 3\right)$

$y - 6 = 6 x - 18$

$y = 6 x - 12$