Question

How do you write the point slope form of the equation given (-3,-3) and slope -1/3?

Answer 1

`y = (-1)/3x-4`

Explanation:

There is a very nifty formula for exactly this situation where we are given the slope `(m)` and one point `(x_1, y_1)` on a straight line and need to find its equation.

`y-y_1 = m(x-x_1)`

`ycolor(red)(-(-3)) = (-1)/3(xcolor(red)(-(-3)))" simplify"`

`ycolor(red)(+3) = (-1)/3(xcolor(red)(+3))`

`ycolor(blue)(+3) = (-1)/3x-1`

`y = (-1)/3x-1color(blue)(-3)`

`y = (-1)/3x-4`

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Note that the formula is based on the formula for slope

`y-y_1 = m(x-x_1)` is derived from `(y-y_1)/(x-x_1) = m`
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We could also have substituted the given values into `y - mx +c`
to find `c` and then substituted again for the final answer.

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