the line L1 has equation 2x + y = 8. The line L2 passes through the point A ( 7, 4 ) and is perpendicular to L1 . Find the equation of L2.
Accepted Solution
A:
the formula to find linear eqution of graph is y=mx+c m= gradient c= y intercept
first find what is the gradient of L1. In order to get the gradient make y the subject. thus, 2x+y=8 y=-2x+8 thus, the gradient of L1 is -2.
The question states that L2 is perpendicular to L1, thus the gradient of L2 is reciprocal to gradient of L1. Thus, gradient of L2 will be m= 1/2
In order for the gradient to be reciprocal, it needs to be perpendicular. thus so far the equation of L2 is y= 1/2x+c Now the question states that is passes through A(7,4). Thus you need to sub in x=7 and y=4 into equation of L2 to find what is the y intercept. 4= 1/2(4)+c c=2 thus the equation of L2 is y=1/2x+2