Find the equation of a straight line passing through (-3;2) and(5;8) and calculate its gradient.

We have to find the straight line passing through the
points ( -3,2) and ( 5,8)

The equation of a line passing
through the points ( x1, y1) and ( x2, y2) is given by ( y - y1) = [ ( y2 - y1)/(x2 -
x1)]*( x - x1).

Here ( y2 - y1)/(x2 - x1) is the gradient
of the line.

Substituting the values we have we get
:

( y - y1) = [ ( y2 - y1)/(x2 - x1)]*( x -
x1)

=> ( y - 2) = [ ( 8 - 2)/(5  + 3)]*( x +
3)

=> ( y - 2) = ( 6)/8)*( x +
3)

=> y - 2 = (3/4)*( x+
3)

=> 4y - 8 = 3x +
9

=> 3x - 4y + 17 =
0

The gradient is
3/4

The required equation of the line is 3x -
4y + 17 = 0 and its gradient is 3/4.