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 negative reciprocals of each other. (flip the sign +/- and the fraction/switch the numerator and the denominator)
For example:
Slope = -2 or [tex]-\frac{2}{1}[/tex]
Perpendicular line's slope = [tex]\frac{1}{2}[/tex] (flip the sign from - to +, and flip the fraction)
Slope = [tex]\frac{1}{3}[/tex]
Perpendicular line's slope = [tex]-\frac{3}{1}[/tex] or -3 (flip the sign from + to -, flip fraction)
y = 3x - 3 The slope is 3, so the perpendicular line's slope is [tex]-\frac{1}{3}[/tex].
Now that you know the slope, substitute/plug it into the equation:
y = mx + b
[tex]y =- \frac{1}{3} x+b[/tex] To find b, plug in the point (3, 1) into the equation, then isolate/get the variable "b" by itself
[tex]1=-\frac{1}{3} (3)+b[/tex]
1 = -1 + b Add 1 on both sides to get "b" by itself
1 + 1 = -1 + 1 + b
2 = b
[tex]y=-\frac{1}{3} x+2[/tex]
