Question

What is the equation in point-slope form of a line that passes through the points (3, −5) and (−8, 4) ?

Answer 1

ANSWER

$y + 5= - \frac{9}{11} (x-3)$

or

$y - 4= - \frac{9}{11} (x + 8)$

EXPLANATION

We want to find the equation in point-slope form of a line that passes through the points (3, −5) and (−8, 4).

The point-slope form is given by;

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

where

$m = \frac{4 - - 5}{ - 8 - 3} = \frac{4 + 5}{ - 11} = - \frac{9}{11}$

is the slope of the line.

If

$(x_1,y_1)=(3,-5)$

The point-slope form is

$y + 5= - \frac{9}{11} (x-3)$

On the other hand, if
$(x_1,y_1)=( - 8,4)$

Then the point-slope form is,

$y - 4= - \frac{9}{11} (x + 8)$

These two equations are the same when simplified.