Question

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

Answer 1

Option $y-5 = -\frac{6}{5} (x-6)$ is the point-slope form for the given point.

Step-by-step explanation:

Step 1:

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

m = $-\frac{6}{5}$ 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 = $-\frac{6}{5}$.

Substituting these values in the equation, we get

$\left(y-y_{1}\right)=m\left(x-x_{1}\right)$ becomes $\left(y-5\right)=-\frac{6}{5} \left(x-6\right)$.

This is the first option that is given.