How do you write the equation in slope intercept form given (4,1):(5,3)?

May 7, 2017

$y = 2 x - 7$

Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
$\text{where m represents the slope and b, the y-intercept}$

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
$\text{where " (x_1,y_1),(x_2y_2)" are 2 coordinate points}$

$\text{the 2 points here are " (4,1)" and } \left(5 , 3\right)$

$\text{let " (x_1,y_1)=(4,1)" and } \left({x}_{2} , {y}_{2}\right) = \left(5 , 3\right)$

$\Rightarrow m = \frac{3 - 1}{5 - 4} = \frac{2}{1} = 2$

$\Rightarrow y = 2 x + b$

$\text{to find b, substitute either of the given points into the}$
$\text{equation and solve for b}$

$\text{using } \left(4 , 1\right)$

$1 = \left(2 \times 4\right) + b$

$\Rightarrow b = 1 - 8 = - 7$

$\Rightarrow y = 2 x - 7 \leftarrow \textcolor{red}{\text{ in slope-intercept form}}$