Question

Write the equation of a line that passws through the point (1,7) and is perpendicular to y=1/2x-5

Answer 1

`y=-2x+5`

Explanation:

For one line to be perpendicular to another, their slopes must multiply to -1. So, we really want the line with slope
`$-1/(1/2)$ = -2$` that passes through the point
`(1, 7)`.

Recall the point-slope form of a line. If you have a point
`$(x_(1), y_(1))$` and a slope
`m`, the line through that point with the given slope is
`$y-y_(1)=m(x-x_(1))$`. Plugging in our given point and slope gives our line:
`y-7=-2(x-1)`(point-slope form).

We can convert this line to slope-intercept form, the most common form by expanding the right side and adding
`7` to get
`y` by itself:

`y-7=-2x+2`

`y=-2x+5`