Question

Please Helpp mee

Find an equation for the line that passes through the point
P (−2,−3)and is perpendicular to the line 4x−5y=4 . Use exact values.

Answer 1

Explanation:

Perpendicular lines are lines whose slopes are negative reciprocals of each other

To find the slope of the line we are given, we can rearrange the equation

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

The slope of this line is
`(4)/(5)`, so the slope of the other line is
`(-5)/(4)`

next, we can use the given point to find the equation
`y = mx +b`

we know m, we can solve for b

`y = (-5)/(4)(x) + b\\-3 = (-5)/(4)(-2) + b\\-3 = (5)/(2) + b\\(-6)/(2) = (5)/(2) + b\\`

`b = (-11)/(2)`

`so,\\y = (-5)/(4)(x) - (11)/(2)`