Determine the gradient or slope and the 𝑦-intercept of the line negative three 𝑦 equals three minus 𝑥.
In order to work out the gradient and the 𝑦-intercept of any equation, we need to rewrite the equation in the form 𝑦 equals 𝑚𝑥 plus 𝑐, where the 𝑚 is the gradient and the 𝑐-value is the 𝑦-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 𝑦 by negative three leaves us 𝑦. Dividing three by negative three gives us negative one. And finally, dividing negative 𝑥 by negative three gives us a third 𝑥.
Rewriting this equation gives us 𝑦 equals one-third of 𝑥 minus one. We know that the coefficient of 𝑥, in this case one-third, is 𝑚 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 𝑐-value or the 𝑦-intercept. So we also know that the 𝑦-intercept of the equation negative three 𝑦 equals three minus 𝑥 is negative one. We can rewrite any linear equation in this form to help us work out the gradient and the 𝑦-intercept.