Question

find the equation of the line that passes trougth the points (6, 3), (9, 15) in slope intercept form

Answer 1

$y=4x-21$

Explanation

Step 1

find the slope

the slope is given by:

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}$

Let

P1(6,3)

P2(9,15)

replacing.

$\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{slope}=\frac{15-3}{9-6}=\frac{12}{3}=4 \\ \text{slope}=4 \end{gathered}$

Step 2

using

slope=4

P1(6,3)

find the equation

$\begin{gathered} y-y_1=m(x-x_1) \\ \text{replacing} \\ y-3=4(x-6) \\ y-3=4x-24 \\ \text{add 3 in both sides} \\ y-3+3=4x-24+3 \\ y=4x-21 \end{gathered}$

I hope this helps you