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{4}{5}[/tex]
Perpendicular line's slope = [tex]\frac{5}{4}[/tex] (flip the sign from - to +, and flip the fraction)
y = 5x + 7 The slope is 5, so the perpendicular line's slope is [tex]-\frac{1}{5}[/tex]
Now that you know the slope, substitute/plug it into the equation:
y = mx + b
[tex]y=-\frac{1}{5} x+b[/tex] To find b, plug in the point (10, 3) into the equation, then isolate/get the variable "b" by itself
[tex]3=-\frac{1}{5} (10)+b[/tex]
3 = -2 + b Add 2 on both sides to get "b" by itself
3 + 2 = -2 + 2 + b
5 = b
[tex]y=-\frac{1}{5} x+5[/tex]
