# How do you write an equation in point-slope form of the line that passes through the given points (-1,-8),(4,-6)?

Mar 3, 2018

$y + 8 = \frac{2}{5} \left(x + 1\right)$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

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

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-1,-8)" and } \left({x}_{2} , {y}_{2}\right) = \left(4 , - 6\right)$

$\Rightarrow m = \frac{- 6 - \left(- 8\right)}{4 - \left(- 1\right)} = \frac{2}{5}$

$\text{using "m=2/5" and } \left({x}_{1} , {y}_{1}\right) = \left(- 1 , - 8\right)$

$y - \left(- 8\right) = \frac{2}{5} \left(x - \left(- 1\right)\right)$

$\Rightarrow y + 8 = \frac{2}{5} \left(x + 1\right) \leftarrow \textcolor{red}{\text{in point-slope form}}$

Mar 3, 2018

$y + 6 = - 0.4 \left(x - 4\right)$

#### Explanation:

Hey!

Well firstly, we know the point-slope form equation:

y−b=m(x−a)

Next, we need to input the values that we are given in the question, in this case (-1,-8), (4,-6). To start, let's solve for m, or slope.

m=(Δy)/(Δx)

Inputting variables:

$m = \frac{\left(- 8\right) - \left(- 6\right)}{\left(- 1\right) - \left(4\right)} = \frac{2}{5} = - 0.4$

Finally, we input the slope value and one of the given points for the $b$ and $a$ values.

$y + 6 = - 0.4 \left(x - 4\right)$

Good luck!