Determine the angle

[Ana.stasia]

The goal was to determine the angle for which the line will have to rotate around a point (2,3) to have m=4.
I calculated that that angle is 90 degrees which is the correct answer, however, it also says alpha 1 = arc tan 1/7, why?
Tg is tan.

 

[AmandasMathHelp]

It looks like you assumed the new line would have a point at (4,0) and then you solved for the slope?? I think you misinterpereted m=4. m is a variable used to represent slope so the slope is actually given to you.. it is just 4. It looks like you have an equation to find the angle between given their slopes so just use the slope of 4 and the slope of 2/3 in that equation!! Also btw the slope of the original line is positive so you're drawing isn't super accurate. Good luck!

 

[Dr.Peterson]

The goal was to determine the angle for which the line will have to rotate around a point (2,3) to have m=4.
I calculated that that angle is 90 degrees which is the correct answer, however, it also says alpha 1 = arc tan 1/7, why?
Tg is tan.

You need to learn to define your terms when asking for help internationally. I've learned from your other questions that m in your country represents the x-intercept, not the slope as it means in America! Apparently your k means slope, and you've found the slopes of the given line and of the line through (2,3) and (4,0) to be 2/3 and -3/2, respectively.

I recognize these as perpendicular, so the line must be rotated through 90 degrees; that can also be found the way you did.

Unfortunately, I have no idea what \(\alpha_1\) means. If it's the tiny angle you show between two lines, what is the second line? It isn't the given line. Please state the entire problem, including how that angle is defined.