Question

Find the point of a line segment with endpoints at (4,-4) and (10,6)

Answer 1

Since this is a line it has a constant velocity or slope, and the line can be expressed as y=mx+b, where m is the slope and b is the y-intercept  (the value of y when x=0)

m=(y2-y1)/(x2-x1)

m=(6--4)/(10-4)

m=10/6

m=5/3, using any point we can then find the y-intercept, I'll use (4,-4)

-4=5(4)/3+b

-4=(20+3b)/3

-12=20+3b

-32=3b

-32/3=b so our line is:

y=(5x-32)/3

So there are infinite points on the line segment defined by the equation above on the interval of x=[4,10]

A point?  How about the midpoint...x=(4+10)/2=7

y(7)=(5*7-32)/3=1

(7,1)