Question

What is the equation of a line that satisfies the given conditions: perpendicular to `y= -2x + 5` and passing through (4, -10)?

Answer 1

`y=1/2x-12`

Explanation:

Perpendicular lines have opposite reciprocal slopes.

The slope of the line `y=-2x+5` is `-2`.

The opposite reciprocal of `-2` is `1/2`, which is the slope of the perpendicular line.

We also know that the line passes through the point `(4,-10)`.

We can use the `y=mx+b` form of the line to determine the equation.

We know that:
`x=4`
`y=-10`
`m=1/2`
And we want to solve for `b`.

`-10=1/2(4)+b`

`-10=2+b`

`-12=b`

The equation of the line is `y=1/2x-12`.