# What is the slope-intercept form of the line passing through  (0, 6)  and  (3,0) ?

Jun 8, 2018

$y = - 2 x + 6$

#### Explanation:

In the slope intercept form $y = m x + b$
m = the slope ( think mountain ski slope. )
b = the y intercept ( think beginning )

The slope can be found by $\frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}}$

putting the values for the points into the equation gives

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

Putting this value for m the slope into an equation with one set of value for a point can be used to solve for b

$6 = - 2 \left(0\right) + b$

This gives

$6 = b$

so

$y = - 2 x + 6$

$\textcolor{red}{y} = - 2 \textcolor{g r e e n}{x} + 6$

#### Explanation:

First of all, You have to use the $\textcolor{B r o w n}{\text{Point-Slope Form}}$ of Linear Equations to get the Slope of the line.

The Point-Slope Form of a Linear Equation is:-

$\textcolor{b l u e}{m} = \frac{\textcolor{R e d}{{y}_{2} - {y}_{1}}}{\textcolor{G r e e n}{{x}_{2} - {x}_{1}}}$

Where $\left(\textcolor{g r e e n}{{x}_{1}} , \textcolor{red}{{y}_{1}}\right)$ and $\left(\textcolor{g r e e n}{{x}_{2}} , \textcolor{red}{{y}_{2}}\right)$ are the points on the line.

So, The Slope for the Required Line

$\textcolor{b l u e}{m} = \frac{0 - 6}{3 - 0} = - \frac{6}{3} = \textcolor{V i o \le t}{- 2}$

Now, We can use the Slope - Intercept Form.

So, The Equation becomes,

$\textcolor{w h i t e}{\times x} \textcolor{red}{y} = \textcolor{b l u e}{m} \textcolor{g r e e n}{x} + \textcolor{S k y B l u e}{c}$

$\Rightarrow \textcolor{red}{y} = - 2 \textcolor{g r e e n}{x} + \textcolor{S k y B l u e}{c}$.

We have been told that The Line has a Point $\left(3 , 0\right)$ on it.

So, The Co-ordinates of that Point must satisfy the Equation.

So,

$\textcolor{w h i t e}{\times x} 0 = - 2 \times 3 + \textcolor{s k y b l u e}{c}$

$\Rightarrow \textcolor{s k y b l u e}{c} - 6 = 0$

$\Rightarrow \textcolor{s k y b l u e}{c} = 6$

So, The Final Equation is,

$\textcolor{red}{y} = - 2 \textcolor{g r e e n}{x} + 6$.

Hope this helps, and I really hope that my colour choice isn't too much bad.