# How do you write the equation in point slope form given (3,8) and (9,0)?

Apr 29, 2018

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

#### 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)

$\text{let "(x_1,y_1)=(3,8)" and } \left({x}_{2} , {y}_{2}\right) = \left(9 , 0\right)$

$\Rightarrow m = \frac{0 - 8}{9 - 3} = \frac{- 8}{6} = - \frac{4}{3}$

$\text{using "(x_1,y_1)=(3,8)" as a point on the line then}$

$y - 8 = - \frac{4}{3} \left(x - 3\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$

Apr 29, 2018

See a solution step below..

#### Explanation:

Recall the equation of a line is;

$y = m x + c$

Where;

$m = \text{slope}$

Also recall that;

m = (y₂ - y_1)/(x₂ - x_1)

where;

y₂ = 0

${y}_{1} = 8$

x₂ = 9

${x}_{1} = 3$

substituting the values

$m = \frac{0 - 8}{9 - 3}$

$m = - \frac{8}{6}$

$m = - \frac{4}{3}$

using these points $\left(3 , 8\right)$ to get the slope form..

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Therefore;

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

As required..