How do you write and equation of a line given (10, –2) with a slope of –1?

Oct 24, 2017

$y = - x + 8$ or graph{y=-x+8 [-22.8, 22.83, -11.4, 11.4]}

Explanation:

The equation of a line is $y = m x + b$.

Since we know that $m = - 1$ ($m$ is the slope), the equation will be $y = \left(- 1\right) x + b$

Put in (10, -2) as $x = 10$ and $y = - 2$:

$- 2 = \left(- 1\right) \cdot 10 + b \to$
$- 2 = - 10 + b \to$ (Multiply $- 1$ and $10$)
$8 = b$ (Add $10$ to both sides)
Flip equation: $b = 8$ (Switch sides)

Whole equation: $y = - x + 8$

$- x$ because $- 1 \cdot x = - x$

Ans: $y = - x + 8$

Hopefully I'm right ;/

Oct 24, 2017

$y = - x + 8$

Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

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

$\Rightarrow y = - x + b \leftarrow \text{ is the partial equation}$

$\text{to find b substitute "(10,-2)" into the partial equation}$

$- 2 = - 10 + b \Rightarrow b = 8$

$\Rightarrow y = - x + 8 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$
graph{-x+8 [-10, 10, -5, 5]}