Question

How do you find the equation of the line parallel to `y=-1/3x+5` that goes through the point `(9, -1)`?

Answer 1

The equation is `y = -1/3x +2`

Explanation:

When two lines are parallel, they have the same gradient (or slope).
In this case the given line `y = -1/3x + 5` has a gradient of `-1/3`.

The new line therefore also has `m = -1/3`
We also have a point (9, -1) which is (x,y)

In the equation of a straight line `y = mx + c` we have three of the four variables and only need to find `c`.

Substituting gives: `-1 = -1/3(9) + c rArr -1 = -3 +c`

`c = -1+3 = 2`

The equation is `y = -1/3x +2`