Answer:
y = -1/2 x + 1
Step-by-step explanation:
Lines that are perpendicular to each other have slopes that are negative reciprocals. You get the negative reciprocal of a number by flipping the fraction for the slope, then changing the positive/negative.
The lines are written in slope-intercept form, y = mx + b.
"x" and "y" are points on the line.
"m" is the slope.
"b" is the y-intercept.
In y = 2x + 8, the slope is 2. Find its negative reciprocal.
Write the slope as a fraction.
[tex]m=2=\frac{2}{1}[/tex]
Flip the fraction.
[tex]m=\frac{1}{2}[/tex]
Change the negative/positive.
[tex]m=-\frac{1}{2}[/tex] This is the slope of the perpendicular line.
Now we need to find the y-intercept, "b", for our line. We know m = -1/2, and we know a random point (6, -2). Points are written (x, y), which mean x = 6 and y = -2. Substitute the values of the point and the slope into y = mx + b.
[tex]y = mx + b[/tex]
[tex]-2 = -\frac{1}{2}*6 + b[/tex] Multiply (-1/2)(6) by combining into the numerator
[tex]-2 = -\frac{6*1}{2} + b[/tex] Simplify numerator
[tex]-2 = -\frac{6}{2} + b[/tex] Reduce fraction
[tex]-2 = -3 + b[/tex] Isolate "b" now
[tex]-2 + 3 = -3 + b + 3[/tex] Add 3 to both sides
[tex]1 = b[/tex] Solved for "b"
[tex]b=1[/tex] Write the variable on the left side for standard formatting
b = 1 and m = -1/2
Substitute them into slope-intercept form for the final answer.
y = -1/2 x + 1
