When you see an equation in the format:
y = mx + c.
Know that the slope = m.
y = -1/5 x + 3.
Therefore slope, m = -1/5. But for the new line to be perpendicular to this, the new line's slope would be the negative reciprocal of -1/5.
That is using the condition for perpendicularity:
m1* m2 = -1. m1 = -1/5.
Where m2 = new slope of the line.
m2 = -1 / (-1/5) = 5.
So the slope of the perpendicular line is 5.
Using the slope and one point format:
y - y1 = m(x - x1) here (x1 , y1) is the point given (2, 8), x1 = 2 , y1 = 8.
m = 5, the new gradient here.
y - 8 = 5(x - 2)
y - 8 = 5x - 10
y = 5x - 10 + 8
y = 5x -2.
So that's the equation of the perpendicular line passing through the given point.
