Another application of the slope equation is when we actually know one point in the slope, but we need to find another point.
So we're still going to use the same equation, slope is change of ys over change of xs, but this time we actually know that our slope is 1/2. So we know that this is equal to 1/2, plugging in the points that we know, so again we can choose either x to go first as long as we are consistent across the board.
So let's say we end up going with this point first, so we end up with 4 minus 1, over x minus 3 is equal to 1/2. So just plug in our slope equation, we now have our ratio 4 minus 1 is 3, so that x minus 3 is equal to 1/2.
There are a number of ways of solving this, we could cross multiply, we can multiply by a common denominator. The easiest way I think to do this is, we know that our numerator is 3, so if we make this numerator 3 as well, we could figure out what our denominators are, the numerator is equal, the denominators have to be equal as well.
So 1/2 is the same thing as 3 over 6. So we have 3 over x minus 3 is equal to 3 over 6, we know that the 3s are equal, so therefore we know that the x minus 3 has to equal 6. So going over here x minus 3 is equal to 6 add 3, you find out that x has to equal 9, so therefore if we have the point 9, 4 the slope is going to be 1/2 between 9 and 3, 1.