Question

Use the coordinates of the labeled points to find a point-slope equation of the line. (3,-4)

Answer 1

slope=-3

y=-3x+5

Explanation:

use two given points (3,-4)(0,5)

5- -4= 9

0-3=-3

9/-3=-3

Answer 2

Answer:
`y+4=-3(x-3)`

Explanation:

The point-slope equation of a straight line is:

`y-y_(1)=m(x-x_(1)  )`

where m is the slope and
`(x_(1), y_(1)  )` are the coordinates of a point in the line.

So, to find the equation, the firs step is to find the slope. We can see in the graphic that the line intercepts the y axis at the point (0, 5), so we're going to use that and the other given point to find the slope:

`m=(y_(2)-y_(1)  )/(x_(2)-x_(1)) =(-4-5)/(3-0) =(-9)/(3)=-3`

Then, you simply substitute the slope and the coordinates of the point and you get the point-slope equation:

`y-(-4)=-3(x-3)\\y+4=-3(x-3)`