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

ANSWER

[tex]y + 5= - \frac{9}{11} (x-3)[/tex]

or

[tex]y - 4= - \frac{9}{11} (x + 8)[/tex]

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;

[tex]y-y_1=m(x-x_1)[/tex]

where

[tex]m = \frac{4 - - 5}{ - 8 - 3} = \frac{4 + 5}{ - 11} = - \frac{9}{11} [/tex]

is the slope of the line.

If

[tex](x_1,y_1)=(3,-5)[/tex]

The point-slope form is

[tex]y + 5= - \frac{9}{11} (x-3)[/tex]

On the other hand, if
[tex](x_1,y_1)=( - 8,4)[/tex]

Then the point-slope form is,

[tex]y - 4= - \frac{9}{11} (x + 8)[/tex]

These two equations are the same when simplified.