Question

Find the slope and y-intercet of the line that is perpendicular to y= 3 x − 3 and passes through the point ( − 8,-2)

Answer 1

Explanation:

If a line has a slope of
`3`, then the line perpendicular to it has a slope of
`-(1)/(3)` (opposite reciprocal).

With this, we can construct a line in slope-intercept form:

`y = mx + b`

Where
`m` is the slope of the line and
`b` is the y-intercept.

We already know the slope of the line, so we can plug it into the equation:

`y = -(1)/(3)x + b`

We also know that the line passes through the point
`(-8, -2)`, so we can plug this into the equation to get
`b`:

`-2 = -(1)/(3)(-8) + b`

`-2 = (8)/(3) + b`

`b = -(14)/(3)`