Question

How do you find slope of the line perpendicular to the line 5x+2y=10?

Answer 1

`"perpendicular slope "=2/5`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"rearrange "5x+2y=10" into this form"`

`"subtract 5x from both sides and divide all terms by 2"`

`2y=-5x+10`

`rArry=-5/2x+5larrcolor(blue)"in slope-intercept form"`

`"with slope "=-5/2`

`"given a line with slope m then the slope of a line"`
`"perpendicular to it is"`

`•color(white)(x)m_(color(red)"perpendicular")=-1/m`

`rArrm_("perpendicular")=-1/(-5/2)=2/5`

Answer 2

The way we find the equations for a family of perpendicular lines is to swap the coefficients on `x` and `y` and negate one of them: `2x - 5y = text{constant}` or `y = 2/5 x + text{constant}`, a slope of `2/5`.