How do I find the equation of a line that's perpendicular to another one?

Remember that the equation of a line is y=mx+c and m is the gradient of the line. The gradient of a perpendicular line will be the negative reciprocal of m ( that just means it will be -1/m). You can then use any other information you've been given in the question to substitute into the equation y=mx+c to get your answer. Let's have a look at an example so you can see how it works:So we have the line y=4x+2 and you want to find the perpendicular line to that which passes through the point (8,1) . The gradient of this line is 4 so the gradient of the perpendicular line will be -1/4 so you have y=-1/4x+c. Now you want to find c. But look, you also have a value for x, 8 and a value for y, 1 so substitute those into your y=mx+c equation. 1=(-1/4)(8)+c and rearrange to find c=3. Pop that into your equation and you get an answer of y=-1/4x+3