From the point where the lines 3x + 2y = 8 and x - y = 9 meet perpendicular line is drawn to the x and y axes. What is their equation
The equations of the lines perpendicular to the x and y axes from the point of intersection of 3x + 2y = 8 and x - y = 9 has to be determined.
First to determine the point of intersection, the equations have to be solved for x and y.
3x + 2y = 8 ...(1)
x - y = 9 ...(2)
(2) gives x = 9 + y
Substitute this in (1)
=> 3(9 + y) + 2y = 8
=> 27 + 5y = 8
=> y = -3.8
x = 5.2
The equation of the line from this point perpendicular to the x-axis has a slope equal to inf.
`(y + 3.8)/(x - 5.2) = 1/0`
=> x = 5.2
The equation of the line from this point perpendicular to the y-axis has a slope equal to 0.
` (y + 3.8)/(x - 5.2) = 0`
=> y + 3.8 = 0
The required line perpendicular to the x-axis is x - 5.2 = 0 and the line perpendicular to the y axis is y + 3.8 = 0