# What is the slope intercept form of the line passing through (2,-2)  with a slope of -2 ?

Feb 29, 2016

$y = - 2 x + 2$

#### Explanation:

$\textcolor{b l u e}{\text{Determine the initial structure of the equation}}$

Standard form of the equation is$\text{ "y=mx+c}$

The slope (gradient) is given as -2 so we now have

$y = - 2 x + c$

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$\textcolor{b l u e}{\text{Determine the value of the constant } c}$

Given that the 'straight' line passes through the point

$\text{ } \left(x , y\right) \to \left(\textcolor{g r e e n}{2} , \textcolor{red}{- 2}\right)$

Substitute in the equation to find the value of c

$\textcolor{red}{y} = - 2 \textcolor{g r e e n}{x} + c \text{ "->" } \textcolor{red}{- 2} = - 2 \left(\textcolor{g r e e n}{2}\right) + c$

$\textcolor{b r o w n}{\text{ } - 2 = - 4 + c}$

Add $\textcolor{b l u e}{4}$ to both sides

color(brown)(" "-2color(blue)(+4)= -4color(blue)(+4)+c

$+ 2 = 0 + c$

$c = 2$
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$\textcolor{b l u e}{\text{Putting it all together}}$

$y = - 2 x + 2$