linear functions (1 Viewer)

[maths lover]

i have reached the end of my past papers and there is one more question which i just cant seem to get. i kinda know how to do it but yeah.
find the equation of any line which makes an acute angle of 15 degrees with 2x-2y+7=0.

 

[Drongoski]

i have reached the end of my past papers and there is one more question which i just cant seem to get. i kinda know how to do it but yeah.
find the equation of any line which makes an acute angle of 15 degrees with 2x-2y+7=0.

Given line has gradient = 1; so it makes an angle of 45 deg with the positive x-axis. Therefore the lines making 15 deg with given line make angle of 30 deg or 60 deg with the positive x-axis with corresponding gradients of 1/root(3) and root(3) resp. The required lines are of form:

 

[maths lover]

oh ok thanks so much but how do we work out the constants

 

[K4M1N3]

To find the constants, i would sub in a value for x into the original equation, find its y,

Then use those values and sub into one of the new equations. Then just solve the equation for the constant.

eg. 2x-2y+7=0 sub x=1....therefore y= 4.5 (or 9/2)

For the new equation, lets take y = sqrt(3)x + D, sub in x=1 and y=4.5

D = (9/2) - sqrt(3)

therefore, y = sqrt(3) + 4.5 - sqrt(3)

 

[Drongoski]

oh ok thanks so much but how do we work out the constants

C and D can be any real number. They are arbitrary constants. They provide the infinite family of straight lines making 15 deg with the given line.

Why don't you just sketch the given straight line. Now draw any straight line making 30 deg or 60 deg with the x-axis.

 

[maths lover]

oh ok so any number placed in the two found lines will achieve the required acute angle. i get it thx's so much