Question

Write an equation in point slope form of a line that passes through the given point and has the given slope

Answer 1

`\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-2})~\hspace{10em} slope = m\implies \cfrac{1}{3} \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-2)=\cfrac{1}{3}[x-(-2)]\implies y+2=\cfrac{1}{3}(x+2)`

Answer 2

`y+2=(1)/(3) (x+2)`

Explanation:

Pre-Solving

We are given that a line has a slope (m) of
`(1)/(3)` and passes through (-2, -2). We want to write this equation in point-slope form.
Point-slope form is given as
`y-y_1=m(x-x_1)` where m is the slope and
`(x_1,y_1)` is a point.

Solving

We can substitute what we know into the equation.

First, substitute
`(1)/(3)` as m.

`y-y_1=(1)/(3) (x-x_1)`

Now, substitute -2 as
`x_1` and -2 as
`y_1`.

We get:

`y--2=(1)/(3) (x--2)`

Simplify.

`y+2=(1)/(3) (x+2)`