Video: Finding the Slope and 𝑦-Intercept of a Straight Line

Determine the gradient and 𝑦-intercept of the line βˆ’3𝑦 = 3 βˆ’ π‘₯.

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Video Transcript

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

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 π‘šπ‘₯ plus 𝑐, where the π‘š 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 π‘₯ by negative three gives us a third π‘₯.

Rewriting this equation gives us 𝑦 equals one-third of π‘₯ minus one. We know that the coefficient of π‘₯, in this case one-third, is π‘š 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 π‘₯ is negative one. We can rewrite any linear equation in this form to help us work out the gradient and the 𝑦-intercept.

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