Match the inequality with its line graph.

a) 2 x > -6

b) x - 4 < -7

c) 6 + x ≤ 3

d) - x - 5 ≤ -2

The answer to your question is below

Step-by-step explanation:

A) 2x > -6

   x > -6/2

   x > -3

   It must be a graph with an open circle starting at -3 and then to the right.

   It is the first graph.

B) x - 4 < -7

   x < -7 + 4

  x < -3

  The graph must be an open circle starting at -3 and pointing to the left.

  it is the second graph.

C) 6 + x ≤ 3

    x ≤ -6 + 3

    x ≤ -3

   The graph must be a closed circle starting at -3 and pointing to the left.

   it is the forth graph.

D) -x - 5 ≤ -2

    -x ≤ -2 + 5

   - x ≤ 3

     x ≥ -3

    The graph must be a closed circle starting at -3 and pointing to the right.

    It is the third graph.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)