Determine the equation of the line that passes through the points (1;2) and (3;4) .Determine the distance between the point (5;6) and the line.

Equation of a line is given by the
equation:

y = mx +
c

Where:

m = slope of the
line

c = y coordinate of the line where it cuts
x-axis.

To find the value of slope of line passing through
the two given points we use the formula:

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

Where the coordinates of the two points are
(x1, y1) and (x2, y2)

Substituting the values of x1, y1,
x2, and y2 in the equation of slope we get:

m = (4 - 2)/(3
- 1)

= 2/2 = 1

To find value
of c, we substitute the values of m, x1and y1 in the general equation of the line. This
gives us:

2 = 1*1 +
c

==> c =
1

Substituting values of m and c in the general equation of
line, the equation of line passing through the two given points
becomes:

y = x + 1

To find the
distance between this line and the point (5, 6), we not that the y coordinate of this
point is 1 more than the x coordinate.

In other words if we
represent the coordinates of this point by (x3, y3):

y3 =
x3 +1

Thus the points satisfy the equation of the given
line.

This means the point lies on the given line.
Therefore:

Distance of the point from the line =
0