Video Transcript
Jacob wants to draw the graph of the linear equation 𝑦 equals three 𝑥 minus four. He plotted the points with 𝑥-coordinates zero, one, two, three, and four but made one mistake. Which point is incorrect? What are the correct coordinates of this point?
When drawing the graph of a linear equation, it’s useful to remember that this graph should form a single straight line. And so if we have plotted a graph that doesn’t form a straight line when we’re expecting one, then we know we’ve made a mistake. Let’s try joining the points that we’ve been given with a straight line. We can do so with four out of the five points. And so the line that we’ve drawn here must be the line 𝑦 equals three 𝑥 minus four. We see that there’s one point that doesn’t lie on this line. That’s point 𝐷. And so point 𝐷 must, in fact, be incorrect.
So with this in mind, how do we find the correct coordinates of this point? Well, in fact, there are two techniques we can use. Point 𝐷 has the coordinates three, four. So this is the one that Jacob calculated with an 𝑥-coordinate of three. So one method we could use would be to substitute 𝑥 equals three into the equation 𝑦 equals three 𝑥 minus four. When we do, we get 𝑦 equals three times three minus four. Well, that’s nine minus four, which is equal to five. And so the correct coordinates of this point are three, five.
Now, we did say that there were two ways of doing this. The second method we could use involves the graph that we’ve already drawn. As such, it’s important not to use this method if we’ve only drawn a graph which contains two points. If our graph only contains two points, we cannot be sure that both those points are correct. What we do is locate a value of 𝑥 equals three on our coordinate axes. We draw a vertical line up from 𝑥 equals three until we hit the line. Then, at this point, we draw a horizontal line along to the 𝑦-axis. And once again, we see that we hit a 𝑦-value of five. So, the correct coordinates of this point are three, five.
