How to find the equation of a line that goes through a point and is perpendicular to an equation?

To be perpendicular to a line, the other line's slope must be the opposite reciprocal of this line's slope. For example, 1/2 and -2 (since -2 = -2/1).

To make sure it goes through the point, plug in the values you have and solve for the y-intercept.

If the point is (3 , 5) for example, and the slope is -2, plug in the x and y values using the formula y=mx+b.

5 = -2(3) + b
5 = -6 + b
b = 11

Therefore, the equation of the line is y = -2x + 11. If you need help with a specific example, let me know.