Video: AQA GCSE Mathematics Higher Tier Pack 5 • Paper 1 • Question 4

Which of these graphs is a sketch of 𝑦 = −𝑥 − 3? Circle the correct letter.

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Video Transcript

Which of these graphs is a sketch of 𝑦 equals negative 𝑥 minus three? Circle the correct letter.

Notice that the question tells us that the graph is just a sketch. We’re not looking for an accurate plot of 𝑦 equals negative 𝑥 minus three. This means we’re just going to be looking at which graph has the correct key features. Remember that the equation of any straight line can be written in the form 𝑦 equals 𝑚𝑥 plus 𝑐, where 𝑚 represents the gradient of the line and 𝑐 is the 𝑦-intercept. These are the key features of any straight line. Let’s compare the equation of the line we’ve been given with the general form.

In our equation, the coefficient, that’s the number in front of the 𝑥, is negative one. So the line 𝑦 equals negative 𝑥 minus three has a gradient of negative one. This means that the line is sloping downwards from left to right. Specifically, for every one unit we move to the right, the line moves one unit down, although we won’t be able to see that exactly on these graphs as they’re just sketches. Comparing the second part of the two equations, we can see that the 𝑦-intercept of our line is negative three, which means it crosses the 𝑦-axis at this value.

Now, let’s look at the four possible graphs we’ve been given. Options b and c can be ruled out because they each have a positive gradient rather than a negative gradient. They slope upwards from left to right rather than downwards. Option a can be ruled out because it has a 𝑦-intercept of negative one rather than a 𝑦-intercept of negative three. Looking at graph d, we can see that it has a negative gradient. And it has a 𝑦-intercept of negative three. Based on these two key features then, graph d is a sketch of the line 𝑦 equals negative 𝑥 minus three.

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