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What is the equation, in slope-intercept form, of the line that is perpendicular to the line y – 4 = –2/3(x – 6) and passes through the point (−2, −2)?
y = –2/3x –10/3
y = –2/3x +10/3
y = 3/2x – 1
y = 3/2x + 1

Respuesta :

lets write the given equation in the y = mx + c form 
y - 4 = -2/3(x-6)
y - 4 = -2/3x + 4
y = -2/3x + 8
therefore the slope is -2/3 and intercept is +8
the perpendicular line passes through x = -2 and y = -2
then if the given graph has a slope of -2/3 the line that is perpendicular to that should have the reciprocal of the gradient and should be in the opposite direction. So m = +3/2
lets substitute x,y and m values for the new perpendicular line
y =mx + c
-2 = 3/2 * -2 +c
-2 = -3 +c
c = -2 +3 
c = 1
Therefore the equation for the perpendicular line is 
y = 3/2x + 1

Answer:

y = 3/2x + 1

Step-by-step explanation: