A line containing the points zero, negative eight and 𝑥, 22 has a slope of five. What is the value of 𝑥?
So in this question, we have two points on a line and we also have the slope of that line. And what we want to do is find the value 𝑥, so one of our coordinates. Well, to help us achieve that and find 𝑥, what we have is a formula. And this formula is the slope formula.
So we have 𝑚, our slope, is equal to 𝑦 two minus 𝑦 one over 𝑥 two minus 𝑥 one, where 𝑦 two, 𝑦 one and 𝑥 two, 𝑥 one are 𝑥- and 𝑦-coordinates of two points on a line. And we have two points on our line, so we can use this. This is also sometimes known as the change in 𝑦 over the change in 𝑥 or the rise over the run. So we can use this to find the 𝑥-coordinate that we want to find, which in this case is gonna be 𝑥 two, because I’ve labelled our coordinates here 𝑥 one, 𝑦 one 𝑥 two, 𝑦 two, by substituting in our values and then rearranging the formula.
So when we substitute in our values, we get five — that’s our slope — is equal to 22 minus negative eight over 𝑥 minus zero. That’s because that’s our 𝑦 two minus 𝑦 one over 𝑥 two minus 𝑥 one. So this is gonna give us five is equal to 30 over 𝑥. And that’s because we had 22 minus negative eight.
Well, if you subtract a negative, it’s the same as adding. So we get 22 add eight, which is 30, and then over 𝑥 because 𝑥 minus zero is just 𝑥. So then to solve for 𝑥, what we first need to do is multiply each side of the equation by 𝑥 to remove it from the denominator. And when we do that, we get five 𝑥 is equal to 30.
And then if we wanna find single 𝑥, well we need to divide five 𝑥 by five to get a single 𝑥. And what we do to one side of the equation we must do to the other. So we divide both sides of the equation by five. And when we do that, we get 𝑥 is equal to six. So therefore, we can say that if a line containing the points zero, negative eight and 𝑥, 22 has a slope of five, the value of 𝑥 will be six.