Question

Write point-slope form of the equation that represents the line that passes through the points (−6, 4) and (4, 2). *Hint: you must find the slope first* Show your work for full credit

Answer 1

ANSWER


`y - 4 = - (1)/(2) (x + 6)`


Step-by-step explanation

The given points are

`(-6,4) \: and \: (4,2)`

First, determine the slope using the formula,


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

`(x_1,y_1)=(-6,4).`
and


`(x_2,y_2)=(4,2)`


Then, the slope becomes,


`m = (2 - 4)/(4 - - 6)`



`m = (2 - 4)/(4 + 6)`



`m = ( - 2)/(10) = - (1)/(5)`


The equation in point slope-form is given by the formula,


`y-y_1=m(x-x_1)`

We substitute the values to get,


`y - 4 = - (1)/(2) (x - - 6)`

Therefore the point-slope form is

`y - 4 = - (1)/(2) (x + 6)`