# How do you write the point slope form of the equation given (-3,4) and (0,3)?

Sep 14, 2016

$y - 3 = - \frac{1}{3} \left(x - 0\right)$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{point-slope form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right)$ a point on the line.

To calculate the slope use the $\textcolor{b l u e}{\text{gradient formula}}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points} .$

here the 2 points are (-3 ,4) and (0 ,3)

let $\left({x}_{1} , {y}_{1}\right) = \left(- 3 , 4\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(0 , 3\right)$

$\Rightarrow m = \frac{3 - 4}{0 + 3} = - \frac{1}{3}$

Using either of the 2 given points for x_1,y_1)

Using (0 ,3) and m$= - \frac{1}{3}$ substitute these values into the point-slope equation.

$y - 3 = - \frac{1}{3} \left(x - 0\right) \leftarrow \text{ point-slope form}$

If we distribute the brackets and rearrange .

or $y = - \frac{1}{3} x + 3 \leftarrow \text{ slope-intercept form}$