Slope-intercept form is:
y = mx + b "m" is the slope, "b" is the y-intercept (the y value when x = 0)
For lines to be perpendicular, their slopes have to be the opposite/negative reciprocals (flipped sign and number)
For example:
slope is 2
perpendicular line's slope is -1/2
slope is -2/3
perpendicular line's slope is 3/2
1.) Isolate the "y" in the given equation.
3x - 2y = 2 Subtract 3x on both sides
-2y = 2 - 3x Divide -2 on both sides
y = -1 + 3/2x
The given line's slope is 3/2, so the perpendicular line's slope is -2/3.
y = -2/3x + b
To find "b", plug in the point (1, 0) into the equation
y = -2/3x + b
0 = -2/3(1) + b
0 = -2/3 + b Add 2/3 on both sides
2/3 = b
[tex]y=-\frac{2}{3}x +\frac{2}{3}[/tex]
2.) Isolate "y"
5x + 6y = 12 Subtract 5x on both sides
6y = 12 - 5x Divide 6 on both sides
y = 2 - 5/6x
The given line's slope is -5/6, so the perpendicular line's slope is 6/5
y = 6/5x + b Plug in the point (3, -1)
-1 = 6/5(3) + b
-1 = 18/5 + b Subtract 18/5 on both sides
-1 - 18/5 = b Make the denominators the same
-5/5 - 18/5 = b
-23/5 = b
[tex]y=\frac{6}{5}x-\frac{23}{5}[/tex]
3. y = 2x - 2
The given line's slope is 2, so the perpendicular line's slope is -1/2
y = -1/2x + b Plug in (-5,5)
5 = -1/2(-5) + b
5 = 5/2 + b subtract 5/2 on both sides
5 - 5/2 = b Make the denominators the same
10/2 - 5/2 = b
5/2 = b
[tex]y=-\frac{1}{2} x+\frac{5}{2}[/tex]
