Let's find the point slope equation for #(6,7)# and #(2,-1)#
Point slope equations are #m = (y-y_1)/(x-x_1)#
So let's find the slope first
#m = (y-y_1)/(x-x_1)#
#m = (7-(-1))/(6-2)#
#m = 8/4 = 2#
Now we have our #m#, let's write our quation
#2 = (y-y_1)/(x-x_1)#
#(y-y_1) = 2 xx (x-x_1)#
So let's solve for #(x_1, y_1)# as #(6,7)#:
#color(green)(y-7 = 2(x-6)#
And also for #(2,-1)#
#color(green)(y+1 = 2(x-2)#
#* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * #
Let's look at our answers:
#A. y - 1 = 2(x + 2)#
#B. y - 7 = (x - 6)#
#C. y - 7 = 2(x - 6)#
#D. y + 1 = (x - 2)#
#E. y + 1 = 2(x - 2)#
#F.y - 7 = (x + 6)#
First, let's get rid of all the ones that have the wrong #m#:
#A. y - 1 = 2(x + 2)#
#color(red)(B. y - 7 = (x - 6)#
#C. y - 7 = 2(x - 6)#
#color(red)(D. y + 1 = (x - 2)#
#E. y + 1 = 2(x - 2)#
#color(red)(F.y - 7 = (x + 6)#
Now let's see which of the remaining ones look like our answers:
#A. y - 1 = 2(x + 2)#
#color(green)(C. y - 7 = 2(x - 6)#
#color(green)(E. y + 1 = 2(x - 2)#
Only two. And they are both options, so it looks like #color(green)(C# and #color(green)(E)# are the right answers
