# What is the point-slope form of the line that passes through (5,6) and (3,10)?

Jun 11, 2018

$y - 6 = - 2 \left(x - 5\right)$

#### Explanation:

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

•color(white)(x)y-y_1=m(x-x_1)

$\text{where m is the slope and "(x_1,y_1)" a point on the line}$

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(5,6)" and } \left({x}_{2} , {y}_{2}\right) = \left(3 , 10\right)$

$m = \frac{10 - 6}{3 - 5} = \frac{4}{- 2} = - 2$

$\text{use either of the 2 given points as a point on the line}$

$\text{using "(x_1,y_1)=(5,6)" then}$

$y - 6 = - 2 \left(x - 5\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$