# How do you write an equation in standard form for a line passing through (3, 4) and (–3, –8)?

$2 x - y - 2 = 0$

#### Explanation:

The equation of line passing through the points $\left({x}_{1} , {y}_{1}\right) \setminus \equiv \left(3 , 4\right)$ & $\left({x}_{2} , {y}_{2}\right) \setminus \equiv \left(- 3 , - 8\right)$ is given by following general formula

$y - {y}_{1} = \setminus \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} \left(x - {x}_{1}\right)$

$y - 4 = \setminus \frac{- 8 - 4}{- 3 - 3} \left(x - 3\right)$

$y - 4 = 2 \left(x - 3\right)$

$y - 4 = 2 x - 6$

$2 x - y - 2 = 0$

Jul 22, 2018

$2 x - y = 2$

#### Explanation:

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

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

$\text{where A is a positive integer and B, C are integers}$

$\text{obtain the equation in "color(blue)"slope-intercept form}$

•color(white)(x)y=mx+b

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

$\text{to calculate m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(3,4)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 3 , - 8\right)$

$m = \frac{- 8 - 4}{- 3 - 3} = \frac{- 12}{- 6} = 2$

$y = 2 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute either of the 2 given points into}$
$\text{the partial equation}$

$\text{using "(3,4)" then}$

$4 = 6 + b \Rightarrow b = 4 - 6 = - 2$

$y = 2 x - 2 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$2 x - y = 2 \leftarrow \textcolor{red}{\text{in standard form}}$

Jul 22, 2018

$2 x - y = 2$

#### Explanation:

If you are given the co-ordinates of two points on a line, here is a good formula to use to get the equation of the line:

$\frac{y - {y}_{1}}{x - {x}_{1}} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Use $\left(3 , 4\right)$ as $\left({x}_{2} , {y}_{2}\right)$

$\frac{y - \left(- 8\right)}{x - \left(- 3\right)} = \frac{4 - \left(- 8\right)}{3 - \left(- 3\right)}$

$\frac{y + 8}{x + 3} = \frac{4 + 8}{3 + 3} = \frac{12}{6} = \frac{2}{1} \text{ } \leftarrow$ this is the slope.

$\frac{y + 8}{x + 3} = \frac{2}{1} \text{ } \leftarrow$ cross multiply

$2 x + 6 = y + 8 \text{ } \leftarrow$re-arrange into standard form.

$2 x - y = 2$