Question

Find the equation of the line through point (1,−5) and perpendicular to y=1/8x+2. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12).

Answer 1

`y = -8x + 3`

Explanation:

Equation of a line:

The equation of a line has the following format:

`y = mx + b`

In which m is the slope and b is the y-intercept.

Perpendicular lines:

When two lines are perpendicular, the multiplication of their slopes is -1.

Perpendicular to y=1/8x+2

This line has slope
`(1)/(8)`

So, for the line we want to find the equation, we have that:

`(m)/(8) = -1`

`m = -8`

So

`y = -8x + b`

Find the equation of the line through point (1,−5)

This means that when
`x = 1, y = -5`. We use this to find b. So:

`y = -8x + b`

`-5 = -8 + b`

`b = 3`

The equation of the line is:

`y = -8x + 3`