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.