Question

y = (-5/4) x + 3write a perpendicular (90° degrees) equation of the given function in the form y=mx +b that passes through the point (5,-1)

Answer 1

Given the equation : y = (-5/4) x + 3

The general form of the line is : y = mx + b

where m is the slope and b is a constant represents y-intercept

so, the slope of the given line is m = (-5/4)

The required line is perpendicular to the given line

Let the slope of the required line is m'

So,

m * m' = -1

m = (-5/4)

So,

`m^(\prime)=-(1)/(m)=-1\text{ / (-5/4)=-1}\cdot(-(4)/(5))=(4)/(5)`

so, the slope of the required line = 4/5

So, the equation of the line : y = (4/5) x + b

To find b substitute with the point (5 , -1)

so, when x = 5 , y = -1

so,

-1 = (4/5) * 5 + b

-1 = 4 + b

-1-4 = b

b = -5

so, the equation of the line is :

`y=(4)/(5)x-5`