Slope-intercept form:
y = mx + b "m" is the slope, "b" is the y-intercept
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
3.) y = 2x - 2
The given line's slope is 2, so the perpendicular line's slope is -1/2
[tex]y=-\frac{1}{2}x+b[/tex] To find "b", plug in the point (-5 , 5) into the equation
[tex]5=-\frac{1}{2}(-5)+b[/tex]
[tex]5=\frac{5}{2}+b[/tex] Subtract 5/2 on both sides
[tex]5-\frac{5}{2}=b[/tex] Make the denominators the same
[tex]\frac{10}{2}-\frac{5}{2}=b[/tex]
[tex]\frac{5}{2}=b[/tex]
[tex]y=-\frac{1}{2}x+\frac{5}{2}[/tex]
4.) -6x + 5y = -10 Get "y" by itself, add 6x on both sides
5y = -10 + 6x Divide 5 on both sides
[tex]y=-2+\frac{6}{5}x[/tex]
The given line's slope is 6/5, so the perpendicular line's slope is -5/6.
[tex]y=-\frac{5}{6}x+b[/tex] Plug in (-2, 5)
[tex]5 = -\frac{5}{6}(-2)+b[/tex]
[tex]5=\frac{10}{6}+b\\ 5=\frac{5}{3}+b[/tex] Subtract 5/3 on both sides
[tex]5-\frac{5}{3} =b[/tex] Make the denominators the same
[tex]\frac{15}{3}-\frac{5}{3}=b\\\frac{10}{3} =b[/tex]
[tex]y = -\frac{5}{6}x+\frac{10}{3}[/tex]
7.) Perpendicular line's slope is -2
y = -2x + b Plug in (1,4)
4 = -2(1) + b
4 = -2 + b
6 = b
y = -2x + 6
8.) Perpendicular line's slope is -1/4
[tex]y = -\frac{1}{4}x+b[/tex] Plug in (-5 , 2)
[tex]2=-\frac{1}{4}(-5)+b[/tex]
[tex]2 = \frac{5}{4}+b[/tex] Subtract 5/4 on both sides
[tex]2-\frac{5}{4}=b[/tex] Make the denominators the same
[tex]\frac{8}{4}-\frac{5}{4}=b[/tex]
[tex]\frac{3}{4}=b[/tex]
[tex]y=-\frac{1}{4}x+\frac{3}{4}[/tex]
