Respuesta :
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 = 8x - 2 The slope is 8, so the perpendicular line's slope is [tex]-\frac{1}{8}[/tex].
Now that you know the slope, substitute/plug it into the equation:
y = mx + b
[tex]y=-\frac{1}{8} x+b[/tex] To find b, plug in the point (-5, -6) into the equation, then isolate/get the variable "b" by itself
[tex]-6=-\frac{1}{8} (-5)+b[/tex] (Two negative signs cancel each other out and become positive)
[tex]-6=\frac{5}{8} +b[/tex] Subtract 5/8 on both sides to get "b" by itself
[tex]-6-\frac{5}{8} =b[/tex] (To combine fractions, they need to have the same denominator, so multiply -6 by 8/8 so that they will have the same denominator)
[tex](\frac{8}{8}) (-6)-\frac{5}{8} =b[/tex]
[tex]-\frac{48}{8} -\frac{5}{8}[/tex] = b Now combine the fractions
[tex]-\frac{53}{8} =b[/tex]
[tex]y=-\frac{1}{8} x-\frac{53}{8}[/tex]
