Question

We want to rewrite the equation y = 2x - 6 in point-slope form, using the point (0, -6)y + 6 = 2(x - 0)y-0 = 2(x + 3)y+6=-2(x-0)y-0 =-2(x-3)

Answer 1

The point-slope form is

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

Where m represents the slope of our function, and (x1, y1) the coordinates of our desired point.

Since our point is (0, -6), then

`\begin{gathered} x_1=0 \\ y_1=-6 \end{gathered}`

Our equation is originally written in slope-intercept form, and the coefficient of x represents the slope of our line, therefore, our slope is equal to 2. With this information, we can rewrite our equation in point-slope form.

`\begin{gathered} (y-(-6))=2(x-0) \\ y+6=2(x-0) \end{gathered}`