Question

Write point slope equation for the line that passes through points (6,5) and (-3,-7)
TT VE

Answer 1

`y-5=(4)/(3) (x-6)`

Explanation:

Pre-Solving

We are given that a line that passes through (6, 5) and (-3, -7). We want to write the 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.

First, we need to find the slope of the line.

Solving

Slope

The slope (m) can be found using the equation
`(y_2-y_1)/(x_2-x_1)` where
`(x_1,y_1)` and
`(x_2,y_2)` are points.

We can label the values of the points:

`x_1=6\\y_1=5\\x_2=-3\\y_2=-7`

Now, substitute into the equation.

`m=(y_2-y_1)/(x_2-x_1)`

`m=(-7-5)/(-3-6)`

`m=(-12)/(-9)`

`m=(4)/(3)`

The slope of the line is
`(4)/(3)`.

Equation

Substitute m as
`(4)/(3)` in
`y-y_1=m(x-x_1)`.

`y-y_1=(4)/(3) (x-x_1)`

Now, substitute 6 as
`x_1` and 5 as
`y_1`.

`y-5=(4)/(3) (x-6)`

Answer 2

The point-slope equation is
`y-5=(4)/(3) (x-6)`

The point-slope form of the equation for a line is given by
`y-y_1=m(x-x_1)`, where
`(x_1,y_1)` is a point on the line and m is the slope.

1. Find the slope

`m=(y_2-y_1)/(x_2-x_1)`

`=((-7)-5)/((-3)-6)`

`=(-12)/(-9)`

`=(4)/(3)`

2. Choose a point on the line, let's say (6,5) and substitute

`y-5=(4)/(3)(x-6)`