Question

Find the equation of the line through the point (–2, –2) that is perpendicular to the line y = 2x – 1.

Answer 1

The gradient of the first line is 2. The new line is perpendicular to the first line. That means the gradient of the new line will be -1/2 because:\[m \times n=-1 \]\[2 \times n=-1\]\[n=\frac{ -1 }{ 2 }\]The next bit is debatable; I was taught in the UK and therefore was taught a different method. But feel free to use your own method to get the equation of the line.
I "pretend" to find the gradient, and I use the coordinates given in the question as well as the new gradient.\[\frac{ y--2 }{ x--2 }=\frac{ -1 }{ 2 }\]\[2y+4=-x-2\]\[2y=-x-2+4\]\[2y=-x+2\]\[y=\frac{ -1 }{ 2 }x+1\]And that last equation is your equation of the line.
I tried to help someone else before with this type of question, but it didn't really work out since I was using a different method. But hopefully we'll get the same answer in the end :)