Processing Math: Done

From Förberedande kurs i matematik 1

If two non-vertical lines are perpendicular to each other, their slopes k1 and k2 satisfy the relation k1k2=−1, and from this we have that the line we are looking for must have a slope that is given by

k2=−1k1=−21

since the line y=2x+5 has a slope k1=2 (the coefficient in front of x).

The line we are looking for can thus be written in the form

y=−21x+m

with m as an unknown constant.

Because the point (2,4) should lie on the line, (2,4) must satisfy the equation of the line,

4=−212+m

i.e. m=5. The equation of the line is y=−21x+5.