In order to find the equation of a line, we need the slope and a point. We already know a point on the line, it is A(2,8), so we just need to calculate the slope.
We are given the line AB, and it has slope
But, the line L is perpendicular to AB, so its slope is the negative reciprocal of the slope of AB. This means that the line L has slope of 3.
Now we can use find the equation of the line using y=mx+b.
`y=mx+b` sub in the point and the slope, solve for b
The line is `y=3x+2` . In standard form, the line is `3x-y+2=0` .
This is my solution:
First find the gradient of AB
A (2,8) B (14,4)
gradient = (4 - 8) / (14 - 2)
= -4 / 12
= -1/ 3
Gradient of perpendicular AB = 3
Since it passes through A
( y - 8)/(x - 2) = 3
y - 8 = 3x - 6
y = 3x + 2