# What is equation of the line in standard form that passes through (2, 7) and ( -4, 1)?

Dec 13, 2017

$y = m x + b$

$y = x + 5$

$x - y = - 5$

#### Explanation:

First, find the slope of the equation using

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

$m = \frac{1 - 7}{- 4 - 2}$

$m = 1$

Second, plug in m (the slope) into the equation $y = m x + b$

So it becomes $y = 1 x + b$

Plug in one of the points into the $x \mathmr{and} y$ values into the equation above and solve for $b .$

So, $\left(7\right) = 1 \left(2\right) + b$

$b = 5$

Finally, plug in the $b$ value into the equation to get the standard form equation.

$y = x + 5 \text{ } \leftarrow$ re-arrange

$x - y = - 5$

Dec 13, 2017

$x - y = - 5$

#### Explanation:

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

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

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

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

â€¢color(white)(x)y=mx+b

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

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{let "(x_1,y_1)=(2,7)" and } \left({x}_{2} , {y}_{2}\right) = \left(- 4 , 1\right)$

$\Rightarrow m = \frac{1 - 7}{- 4 - 2} = \frac{- 6}{- 6} = 1$

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

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

$\text{using "(2,7)" then}$

$7 = 2 + b \Rightarrow b = 7 - 2 = 5$

$\Rightarrow y = x + 5 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$\Rightarrow x - y = - 5 \leftarrow \textcolor{red}{\text{in standard form}}$