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{2}{5}[/tex]
Perpendicular line's slope: [tex]\frac{5}{2}[/tex] (flip the sign from - to +, and flip the fraction)
y = -3x - 4 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 (4, -3) into the equation, then isolate/get the variable "b" by itself
[tex]-3=\frac{1}{3} (4)+b[/tex]
[tex]-3=\frac{4}{3} +b[/tex] Subtract 4/3 on both sides to get "b" by itself
[tex]-3-\frac{4}{3} =b[/tex] To combine fractions, they must have the same denominator.
[tex](\frac{3}{3} )(-3)-\frac{4}{3} =b[/tex]
[tex]-\frac{9}{3} -\frac{4}{3} =b[/tex] Now combine the fractions
[tex]-\frac{13}{3} =b[/tex]
[tex]y=\frac{1}{3}x-\frac{13}{3}[/tex]
