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 = [tex]\frac{1}{3}[/tex]
Perpendicular line's slope = [tex]-\frac{3}{1}[/tex] or -3
Slope = -2 or [tex]-\frac{2}{1}[/tex]
Perpendicular line's slope = [tex]\frac{1}{2}[/tex]
[tex]y=\frac{1}{3} x+5[/tex] The given line's slope is [tex]\frac{1}{3}[/tex], so the perpendicular line's slope is -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, 9) and isolate/get the variable "b" by itself in the equation
9 = -3(1) + b Add 3 on both sides to get "b" by itself
9 + 3 = -3 + 3 + b
12 = b
y = -3x + 12
