Question

Write an equation of the line that goes through the point ( 15, 1 ) and is perpendicular ro the line y = 5x - 1

Answer 1

We are given the line

y = 5x - 1

The slope here is the coefficient of x, and that is 5.

Note that the slope of a line perpendicular to another one is a negative inverse of the first one. That means when two lines are perpendicular to each other, their slopes are negative inverses of each other. Hence, the slope of a line perpendicular to the one given is

`m=-(1)/(5)`

Having determined thew slope of the other line, and it passes through the point (15, 1), we shall now use the known values to find the equation of the line. The known values are x, y and m

`\begin{gathered} y=mx+b \\ x=15,y=1,m=-(1)/(5) \\ 1=-(1)/(5)(15)+b \\ 1=-3+b \\ 1+3=b \\ b=4 \\ \text{Therefore, having derived m and b, the equation becomes;} \\ y=-(1)/(5)x+4 \end{gathered}`

The equation of the line is show above as,

y = -1/5x + 4