00:01
We have been given a graph where we have a line ab that's intersected by a line cd.
00:10
There's a 45 degree angle between line cd and line ab, and they intersect at a point of 5, 4.
00:19
We're also told that line ab has an equation of 5y minus 3x minus 5 equals 0.
00:27
From that equation, we could write that equation in slope intercept form by adding the 3x over and then dividing both sides by 5.
00:44
That would let us know that the slope of ab is equal to 3 fifths.
00:51
The angle that exists between two lines can be found by saying that the tangent of that angle is equal to the difference in the slopes of the two lines over 1 plus the product of their slopes.
01:20
We already know that the slope of one of the lines is 3 fifths.
01:27
We're trying to figure the slope of the other.
01:29
I'll call 3 fifths m1 and m2 is the slope or gradient of line cd.
01:39
Tangent of 45 degrees then should equal m2, which we don't know, minus m1, which is 3 fifths, over 1 plus 3 fifths times m2.
02:08
Tangent of 45 degrees, though, is 1, so let's just replace it.
02:18
Since we have a fraction equal to 1, that is going to indicate that the fraction has the same numerator and denominator, because fractions equal to 1 have the same top and bottom.
02:29
So let's set the numerator and denominator equal to each other...