Question

How do you write the equation of a line in slope intercept form that is parallel to the line `y=1/3x+5` and passes through (-9, 5)?

Answer 1

`y = -3x - 22`

Explanation:

If you have the slope of a line, `m` and one point, `(x_1, y_1)` the easiest way to find its equation is by using the formula: `y - y_1 = m(x - x_1)`

Let's find the slope first. If two lines are perpendicular, then the one slope is the negative reciprocal of the other.. ie `m_1 xxm_2 = -1`

The line we want to know about is perpendicular to a line with a slope of `1/3`, so the new slope is -3. We have the point `(-9,5)`

Substitute into `y - y_1 = m(x - x_1)` and simplify
`y - 5 = -3(x - (-9)) rArr y - 5 = -3(x + 9)`

`y = -3x - 27 + 5`

`y = -3x - 22`