Write an equation of the line that is perpendicular to the line y = 2x + 8, and which passes through the point (6,-2).
a) y = 2x + 4
b) y = -2x + 1
c) y = -
1
2
x - 4
d) y = -
1
2
x + 1

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.

Flip the fraction.

Change the negative/positive.

   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.

     Multiply (-1/2)(6) by combining into the numerator

     Simplify numerator

      Reduce fraction

        Isolate "b" now

     Add 3 to both sides

       Solved for "b"

        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

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total