If a line has a positive slope, what can be said of the angle it makes with the positive 𝑥-axis?
A positive slope means the line is increasing from left to right. Now it can’t tilt; it can’t move. However, if the line goes directly vertical up and down, it’s considered an undefined slope. Or, if it were horizontal, it would be zero slope.
So it has to be somewhere between the vertical line and the horizontal line. This means the angle that would be formed between the positive slope and the positive 𝑥-axis is that — it must be an acute angle. It must be less than ninety degrees. Because like we said, it has to be between the undefined slope and the zero slope. So it has to stay essentially with the ninety degrees. So it can’t be exactly ninety degrees because that would be the up and down undefined slope, and it couldn’t be zero degrees because that’s a zero slope.
So if we need a positive slope, then it needs to stay between those. So it must be an acute angle, which is between zero and ninety degrees.