If l is a line through the points (2,5) and (4,6) what is the value of k so that the point of coordinates (7,k) is on l.

W have the points: (2,5) and (4,6) passes through a lint L
.

We need to determine k values such that ( 7, k) is on the
line:

First we will determine the equation for the line
L:

( y- y1) = m (x-x1)   where (x1,y1) is any point of the line and
m is the slope:

==> ( y-5) = m (x-2)
............(1)

Now we will determine the
slope:

m= ( y2-y1)/(x2-x1) = ( 6-5)(4-2) =
1/2

==> m = 1/2

==> (y-5)
= (1/2) ( x-2)

==> y-5 = (1/2)x -
1

==> y= (1/2)x - 1
+5

==> y= (1/2)x + 4

Now we know
that the point ( 7, k ) passes through the line:

Then ( 7,k) should
verify the equation for the line:

==> k= (1/2)*7 +
4

==? k = 7/2 + 4 = 15/2 =
7.5

==> k =
7.5