# How do you write the equation in slope intercept form given (3/4,5/2) and ( - 7/8, 3/2)?

May 31, 2018

$y = \frac{8}{13} x + \frac{53}{26}$

#### Explanation:

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

•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)

$\text{let "(x_1,y_1)=(3/4,5/2)" and } \left({x}_{2} , {y}_{2}\right) = \left(- \frac{7}{8} , \frac{3}{2}\right)$

$m = \frac{\frac{3}{2} - \frac{5}{2}}{- \frac{7}{8} - \frac{3}{4}} = \frac{- 1}{- \frac{13}{8}} = \frac{8}{13}$

$y = \frac{8}{13} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

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

$\text{using "(3/4,5/2)" then}$

$\frac{5}{2} = \frac{6}{13} + b \Rightarrow b = \frac{5}{2} - \frac{6}{13} = \frac{53}{26}$

$y = \frac{8}{13} x + \frac{53}{26} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$