Question

Find the equation of a line that is perpendicular to 2x+5y=12 and goes through the point (4,5)

Answer 1

First I would put the equation into y = mx + b form.

`5y = - 2x + 12`

`y = ( - 2)/(5) x + (12)/(5)`
The slope of a perpendicular line will be a negative reciprocal of the line it is perpendicular too. The slope for the new equation will be 5/2.
Then we can use the point given to find the y intercept(b).

`5 = (5)/(2) (4) + b`

`5 = 10 + b`

`- 5 = b`
Now we can write the final equation.

`y = (5)/(2) x - 5`