Question

What is the slope of a line perpendicular to `x+2y=7`?

Answer 1

The slope perpendicular to the equation is 2.

Explanation:

First, find the slope of the equation by setting it into slope-intercept form, `y = mx + b`:
`x + 2y = 7`

Subtract `color(blue)x` from both sides:
`x + 2y quadcolor(blue)(-quadx) = 7 quadcolor(blue)(-quadx)`

`2y = 7 - x`

Divide both sides by `color(blue)2`:
`(2y)/color(blue)2 = (7-x)/color(blue)2`

`y = 7/2-1/2x`

We know that the slope of a slope-intercept equation is the value multiplied by `x`. That means the slope of the equation is `-1/2`.

Now to find the slope perpendicular to the equation, we find the negative reciprocal, or switching the sign and doing `1` over the slope.

So:
`(-1)/(-1/2) = -2`

Therefore, the slope perpendicular to the equation is 2.

Hope this helps!