Question

How do you write an equation of a line passing through (2, 4), perpendicular to `10x - 5y = 8`?

Answer 1

`y=-1/2x+5`

Explanation:

First, convert `10x-5y=8` into the form of `y=mx+b`

`10x-5y=8`

`-5y=8-10x`

`y=2x-8/5`

The perpendicular line to `y=2x-8/5` will have a slope equal to `-1/2`, because perpendicular lines' slopes have a product of `-1`.

The new line will be

`y=-1/2x+b`

We know that it passes through `(2,4)`, so we can plug that into the new equation.

`4=-1/2*2+b`

`4=-2+b`

`b=6`

So, the new equation of the line will be

`y=-1/2x+5`

Answer 2

`y=-1/2x+5`

Explanation:

`"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`

`"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 "10x-5y=8" into this form"`

`rArr-5y=-10x+8rArry=2x-8/5rArrm=2`

`rArrm_(color(red)"perpendicular")=-1/2`

`rArry=-1/2x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(2,4)" into the partial equation"`

`4=-1+brArrb=4+1=5`

`rArry=-1/2x+5larrcolor(red)"perpendicular equation"`