Write the equation of the line perpendicular to -2x+4y=8 that passes through (-3,1). write you answer in slope-intercept form. show your work!

y = -2x - 5

Step-by-step explanation:

First, find the slope of the initial equation by writing in slope-intercept form

y = mx + b

-2x + 4y = 8

+2x         +2x           (Add 2x to both sides)

         4y = 8 + 2x

         4y = 2x + 8    (Rearrange the equation)

          4      4      4   (Divide each term by 4)

          y = 1/2x + 2

When comparing the the equation y = mx+b, where m is your slope,

the slope of this equation is 1/2. To find the line perpendicular, the slope will be the reciprocal with the "opposite sign". The reciprocal of 1/2 is 2 and since the original was positive, the perpendicular slope must be negative.

Begin to write your equation with the slope m = -2 using point slope formula: y - y1 = m (x - x1)

y -  1  = -2(x - (-3)    (Plug in values)

y -  1  = -2(x + 3)     (Distribute negative inside parentheses)

y -  1 =  -2x - 6       (Distribute -2 to both terms inside parentheses)

  + 1           + 1        (Add 1 to both sides)

  y = -2x - 5

Check your answer by filling in the original point (-3, 1)

y = -2x - 5

1 = -2(-3) - 5      (Plug in values)

1 = 6 - 5             (Multiply)

1 = 1

 

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