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General equation of line y=mx+c 1. Find the gradient(m1) of the line. 2. Find the negative reciprocal(m2) of that: -1/m1(gradient) All lines with that negative reciprocal are perpendicular. (3.) If you want to find a particular perpendicular line, substitute, into general equation, the given (X, Y) coordinates and m2 (found in step 2), and use them to find c. This c will give you a unique equation.
When you see perpendicular paired up with an equation of a line. Alarm bells should be ringing to you reminding you that it involves the negative reciprocal (-1/slope) The slope of y=4x+2 is 4 so the perpendicular line will have a slope of -1/4. Thé perpendicular line equation will be of the format y=-1/4x +b If you have the coordinate points you can then calculate b (which can be negative or positive)
The formula for finding the perpendicular to a line is -1/slope. In your case of y=4x + 2, the slope is 4, so the equation would be y=-(1/4)x + b. If you are given a coordinate through which the perpendicular must pass, you can substitute the x and y values into your new equation to find b.
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