Example  I:
The slope of a line passing through (5,3) and (6,a) is 8/3. Find the value of a.
Solution:
Given that,
The line is passing through (5,3) and (6,a)
Therefore, the slope of these two points is
m = (y_{2}  y_{1}) / (x_{2}  x_{1})
m = (a  3) / (6  5)
m = a  3
Given that, m = 8/3
a  3 = 8/3
a = 8/3  3
a = (8  9)/3
a = 1/3
Example  II:
The line 4x + 3y  5 = 0 is perpendicular to 3x  ay + 7 = 0, find the value of a.
Solution:
Let the slope of 4x + 3y  5 = 0, be m_{1},
Then m_{1} = x coefficient / y coefficient.
i.e., m_{1} = 4/3
If m_{2} is the slope of 3x  ay + 7 = 0, then
m_{2} = 3 / a
m_{2} = 3/a
Given that the lines are perpendicular, we know that the product of the perpendicular lines slope is equal to 1.
i.e., m_{1}m_{2} = 1
4/3 * 3/a = 1
4/a = 1
a = 4
Direction: Solve the following problems. Also write at least 10 examples of your own.
