Question

Given m = -6/5 and the point (6, 5), which of the following is the point-slope form of the equation?

y - 5 = -6/5(x - 6)


y - 5 = 6/5(x + 6)


y - 6 = 6/5(x - 5)


y + 6 = 6/5(x + 5)

Answer 1

Option
`y-5 = -(6)/(5) (x-6)` is the point-slope form for the given point.

Explanation:

Step 1:

As we have the slope, m and a coordinate we can use the point-slope form to find the equation.

m =
`-(6)/(5)` and the coordinate is (6, 5) assume this to be (
`x_(1), y_(1)`).

The point-slope form is
`\left(y-y_(1)\right)=m\left(x-x_(1)\right)`.

Step 2:

For the given point,
`x_(1) = 6` and
`y_(1) = 5` and m =
`-(6)/(5)`.

Substituting these values in the equation, we get

`\left(y-y_(1)\right)=m\left(x-x_(1)\right)` becomes
`\left(y-5\right)=-(6)/(5) \left(x-6\right)`.

This is the first option that is given.