How do you write the equation in point slope form given (-1,10) and (5,8)?

You already have the "point" part, now we just need to settle the "slope" part.

The slope of the straight line is a measure of how much the vertical component (#y#) changes for every unit that the horizontal component (#x#) changes. For example. a slope of #2# means that for every one unit increment in #x#, there will be a #2# units increment in #y#.

A large slope value corresponds to a steep one. A slope of #3# is steeper than a slope of #2#.

Slopes can also be negative; it just means that as #x# increases, #y# decreases. A line with a slope of #-2# means that every increment of #1# unit in #x# results in a decrease of #2# units in #y#.

Straight lines with positive slope run from the bottom-left of the graph to the top-right, while straight lines with negative slope run from the top-left of the graph to the bottom-right.

To calculate the slope, #m#, of a line from 2 points, we need to compare the change in the #y# value to the change in the #x# value

#m = frac{"Change in " y}{"Change in " x}#

#= frac{8-10}{5-(-1)}#

#= frac{-2}{6}#

#= -frac{1}{3}#

Now to write in point slope form, you first choose a point, #(x_1,y_1)#. For simplicity, you pick either #(5,8)# or #(-1,10)#, but any other point on the line will also give you a "different" but correct answer. With the gradient #m#, you just have to write

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

So using the two points above as examples. The answer is

#y - 8 = -1/3 (x - 5)#

or

#y - 10 = -1/3 (x + 1)#