How do you find the equation of a line that Contains point (5, -3) and is perpendicular to y=5x?

1 Answer
Jan 18, 2016

y=-1/5x -2

Explanation:

For finding an equation of a perpendicular line, we start with finding the slope of the given line. Slope of the perpendicular line is negative reciprocal of the given slope. For example, if the slope is m then the slope of the perpendicular would be -1/m

Equation of the form y=mx+b has the slope as m

Using this knowledge, we can see that the slope of the line y=5x is 5

The slope of the perpendicular line is -1/5

We can say our line would be

y=-1/5x + b

We need to find b to find the equation. This is where the point(5,-3) is used.

Let us substitute the value x=5 and y=-3 in the equation y=-1/5x+b

We get,
-3=-1/5(5)+b
-3=-1+b
Add 1 to both the sides.

-3+1=b

-2=b

Our equation becomes y=-1/5x -2