# What is the equation of the line passing through (8,2), (5,8)?

Nov 21, 2015

$\textcolor{b r o w n}{y = \left(- 2\right) x + 18}$

#### Explanation:

Assumption: This is for a strait line graph (not stated in question)

Let $\left({x}_{1} , {y}_{1}\right) \to \left(8 , 2\right)$
Let $\left({x}_{2} , {y}_{2}\right) \to \left(5 , 8\right)$

Using standard equation for strait line graph.

$y = m x + c$.............(1)

$\textcolor{g r e e n}{\text{Method: determine gradient(m) Then substitute in equation (1) with}}$
$\textcolor{g r e e n}{\text{known values for x and y to determine the constant's value.}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{To find the gradient}}$

gradient $= m = \left(\text{change in Up or down")/("change in along}\right)$

$\textcolor{b r o w n}{m} = \frac{{y}_{2} - {y}_{1}}{{c}_{2} - {x}_{1}} = \frac{8 - 2}{5 - 8} = \frac{6}{- 3} = \textcolor{b r o w n}{- 2} \textcolor{w h i t e}{\ldots}$.......(2)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{To find the value of c}}$

Substitute for m and$\textcolor{w h i t e}{.} \left({x}_{1} , {y}_{1}\right)$ into equation (1)

$2 = \left(- 2\right) \left(8\right) + c$

$\textcolor{b r o w n}{c = 18}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Bring it all together}}$

$\textcolor{b r o w n}{y = \left(- 2\right) x + 18}$

$\textcolor{g r e e n}{\text{Note: as the gradient is negative it is a downward slope}}$
$\textcolor{g r e e n}{\text{as you move from left to right.}}$