Given that that correlation coefficient can only be between -1 and 1, it can never increase the steepness of the slope when calculating the steepness of a slope in a regression line.
Say correlation coefficient r = 0.946, standard deviation along the x-axis Sx = 0.816, and standard deviation along y-axis is Yx = 2.160 (values same as in reference Khan Academy video to follow along with example) then slope m = r(Sx/Sy). Here Sx/Sy will be the slope if the correlation coefficient is 1 and all the data plots match perfectly to the line. When we multiply it by r=0.946 however, the steepness of the slope decreases. My question is, how do we know that the only possibility here is where the slope decreases and not increases? The correlation coefficient only indicates how accurate the data plot is compared with the regression line, it says nothing about in which direction (more steep or less steep) the inaccuracy points to. So why are we multiply r with Sx/Sy when we know a r with a absolute value of less than 1 can only decrease the steepness of the slope but never increase it?
Edit: This is how Sal Khan explains the concept in his lesson video, that the slope decreases after multiplying by the correlation coefficient.