Question

Line k has a slope of -5. Line i is perpendicular to line k and passes through the point (5,9). Create the equation for line j.

Answer 1

Therefore the equation of the line required is given by
`y = (1)/(5) x + 8`

Explanation:

i) Line k has a slope of
`m_(1)` is equal = -5

ii) Line i is perpendicular to line k and passes through the point (5,9)

Let the slope of line i be
`m_(2)`.

Therefore
`m_(1) * m_(2) = -1 \Rightarrow m_(2)* (-5) = -1 \therefore m_(2) = (-1)/(-5) = (1)/(5)`

iii) using the general equation for a line y = mx + c and substituting
`m_(2)` value and the value of a and y given by the co-ordinates through which the line passes

therefore we get

`9 = (1)/(5) * 5 + c \Rightarrow 9 = 1 + c \therefore c = 8`

Therefore the equation of the line required is given by
`y = (1)/(5) x + 8`