Question

How do you write the equation of the line passing through `( 3, - 2)` and parallel to : `x + 7y - 5 = 0`?

Answer 1

`7y + x + 11 = 0`

Explanation:

We first find the slope of the original line, then use our slope and point to find our equation.

Slope-intercept form is a way of writing your linear equation. It is of the form `y = mx + b`, where `m` is the slope and `b` is the initial value.

If two lines are parallel, then they have the same slope. Our given equation is `x + 7y - 5 = 0`, which can be written in slope-intercept form as `y =- 1/7 x + 5/7`. The slope of both lines, then, is `-1/7`.

Now we use slope-intercept form again to find our new equation given our point `(3, -2)` and our slope `m = -1/7`. We plug in and solve for `b`,

`y = mx + b`
`y = -1/7 x + b`
`-2 = -1/7 (3) + b`
`-2 + 3/7 = b`
`b = -11/7`

Thus, our desired equation is `y = -1/7 x - 11/7`. Our original equation was in standard form, so we should put our answer in standard form.

`y = -1/7 x - 11/7`
`7y = -x - 11`
`7y + x + 11 = 0`

Our final answer is `7y + x + 11 = 0`.