Find the point-slope equation for the line that passes through the points (5,19) and (-5,-1).

y - 19 = 2(x - 5)

Step-by-step explanation:

The point slope form is expressed as

y - y1 = m(x - x1)

Where

m represents slope

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The given points are (5,19) and (-5,-1)

y2 = - 1

y1 = 19

x2 = - 5

x1 = 5

Slope,m = (- 1 - 19)/(- 5 - 5) = - 20/- 10 = 2

To determine the equation, we would substitute x1 = 5, y1 = 19 and m= 2 into the point slope form equation. It becomes

y - 19 = 2(x - 5)

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0