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Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
For lines to be perpendicular, their slopes have to be the negative reciprocal of each other. (Basically flip the sign +/- and the fraction(switch the numerator and the denominator))
For example:
Slope = 2 or
Perpendicular line's slope = (flip the sign from + to -, and flip the fraction)
Slope =
Perpendicular line's slope = (flip the sign from - to +, and flip the fraction)
y = 1/3x + 4 The slope is 1/3, so the perpendicular line's slope is or -3.
Now that you know the slope, substitute/plug it into the equation:
y = mx + b
y = -3x + b To find b, plug in the point (1, 2) into the equation, then isolate/get the variable "b" by itself
2= -3(1) + b Add 3 on both sides to get "b" by itself
2 + 3 = -3 + 3 + b
5 = b
y = -3x + 5