Question

How do you find the slope that is perpendicular to the line `4x-2y=10`?

Answer 1

`m_1 = 2 and m_2 = -1/2`

Explanation:

`4x-2y =10" "larr` change into slope-intercept form

`4x -10 = 2y" "div2`

`2x-5 = y`

`y = 2x-5`

This is now in the form `y = mx +c`
It gives the slope and the y-intercept immediately

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Recall: Slopes which are perpendicular are negative reciprocals of each other. Their product is -1.

Here are some examples:

`3/1xx-1/3 = -1;color(white)(x)-3/2xx2/3 = -1; color(white)(x) -4 xx1/4 = -1`

In general if one slope is `a/b`, the other will be `-b/a`
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In `y = 2x-5, color(white)(xxxxxxx)m = 2`

The slope perpendicular to 2 is`-1/2`

Note:
`-1/2 = (-1)/2 = 1/-2" "larr` the negative sign can be anywhere