Question

Which equations represent the line that is perpendicular to the line 5x – 2y = -6 and passes through the point (5,-4)?

Answer 1

Answer:

None of these apply

Step-by-step explanation:

Step 1: Bring the equation into the form of y=mx+c

5x-2y = -6

-2y = -6-5x

y = 6+5x

       2

y = 5/2x + 3

Step 2: Identify the slope (m)

Slope is the number with x (5/2)

Step 3: Find slope of the perpendicular line.

Slope of line 2 (perpendicular line) = -1/slope of line 1

m2 = -1/m1

m2 = -1/5/2

m2 = -2/5

Step 4: Find the y-intercept of the perpendicular line,

slope = -2/5

x and y coordinates = (5, -4)

y = mx + c

-4 = -2/5 (5) +c

-4 + 2 = c

c = 2

Step 5: Form equation of perpendicular line

y = mx + c

y = -2/5x + 2

Step 6: Check all equations and match with y = -2/5x + 2

a) y = x - 2 (It does not apply because this equation does not have a slope and y-intercept is not the same).

b) 2x + 5y = -10

   5y = -10 -2x

   y = -2/5x - 2 (This does not apply because the y-intercept does not match-it should be +2))

c) 2x - 5y = -10

   -5y = -10 - 2x

     y = 2/5x + 2 (This does not apply because the slope does not match-it should be -2/5)

d) y + 4 = (x - 5)

  y = x-5-4

  y = x-9 (This does not apply as the slope and y - intercept do not match)

e) y - 4 = (x + 5)

  y = x + 9 (This does not apply as the slope and y - intercept do not match)

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