Question

Which equations represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point

(5,-4)? Select three options.

Answer 1

Answer: 2x+5y+10=0

Explanation:

The equation of the given line :
`5x - 2y = -6` which can be written as
`2y=5x+6` or
`y=(5)/(2)x+3` . (i)

Linear equation :
`y=mx+c`, where m= slope and c = intercept.

Comparing this to (i), we get
`m=(5)/(2), c=3`

Let
`m_1` be the slope of the line perpendicular to the line 5x - 2y = -6 and passes through the point (5,-4).

Since, the product of slopes of two perpendicular lines is -1.

So,

`(5)/(2)* m_1=-1\\\\\Rightarrow\ m_1=-(2)/(5)`

Equation of line passes through (a,b) and have slope n is given by :-

`(y-b)=n(x-a)`

So, Equation of line passes through (5,-4) and have slope
`(2)/(5)` would be

`(y-(-4))=(-2)/(5)(x-5)\\\\\Rightarrow\ 5(y+4)=-2(x-5)\\\\\Rightarrow\ 5y+20=-2x+10\\\\\Rightarrow\ 2x+5y+10=0`

Required equation :
`2x+5y+10=0`