Question

Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Check all that apply.

y = –x – 2
2x + 5y = −10
2x − 5y = −10
y + 4 = –(x – 5)
y – 4 = (x + 5)

Answer 1

Writing
`5x-2y=-6` in slope-intercept form:

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

The slope of the line is the number before "x", which is
`(5)/(2)`.

The slope of the perpendicular to this line is the negative reciprocal of this.

So the slope of perpendicular is
`-(2)/(5)`.

To find the equation of the perpendicular line, we need a point. It is given as
`(5,-4)` where
`x_(1)=5` and
`y_(1)=-4`.

Now we use the point-slope form of a line to figure out the equation:

`y-y_(1)=m(x-x_(1))`

Plugging in the values of
`x_(1)` and
`y_(1)` and
`m=-(2)/(5)`, gives us:

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

Multiplying everything by 5 [to get rid of the denominator] and re-arranging gives us:

`y+(2)/(5)x=-2\\5y+2x=-10\\2x+5y=-10`.

THIS IS THE SECOND OPTION.

ANSWER:
`2x+5y=-10`