### Video Transcript

Determine the gradient or slope and the π¦-intercept of the line negative three π¦ equals three minus π₯.

In order to work out the gradient and the π¦-intercept of any equation, we need to rewrite the equation in the form π¦ equals ππ₯ plus π, where the π is the gradient and the π-value is the π¦-intercept.

In this question, there is only one step, and that is to divide the left-hand side and the right-hand side by negative three. Dividing negative three π¦ by negative three leaves us π¦. Dividing three by negative three gives us negative one. And finally, dividing negative π₯ by negative three gives us a third π₯.

Rewriting this equation gives us π¦ equals one-third of π₯ minus one. We know that the coefficient of π₯, in this case one-third, is π the gradient or the slope of the line. So the gradient or slope is equal to a third.

The minus one or negative one is our π-value or the π¦-intercept. So we also know that the π¦-intercept of the equation negative three π¦ equals three minus π₯ is negative one. We can rewrite any linear equation in this form to help us work out the gradient and the π¦-intercept.