Question

Write an inequality for the graph.

A) -6x+5y>=-30
B)-6x+5y<=-30
C)5x-6y<=-30
D)5x-6y>=-30

Answer 1

Answer: 5x-6y >= -30

Explanation:

Pick two points from the graph to frame the equation of the line = (0,5) and (-6,0)

Frame the equation y=mx+b, where m is the slope and b is the y-intercept

The y-intercept is the point where the graph crosses y-axis and it is equal to 5.

slope m = y2-y1/x2-x1 = 0-5/-6-0 = 5/6

Equation becomes y = 5/6x+5

Multiply the whole equation by 6

6y+5x = 30

Subtract 5x on both sides

-5x+6y = 30

Multiply whole equation by -1

5x-6y = -30

Now we look at the shaded part and confirm the inequality

The shaded part contains (0,0)

So we plug in 0 for x and 0 for y

5(0) - 6(0) = -30

0 >= -30 is true

So inequality becomes 5x-6y >= -30

Answer 2

Use y = mx + b to determine the equation of the graph, then decided the inequality symbol.

m = +5/+6 =
`(5)/(6)` b = 5

y =
`(5)/(6)`x + 5

6y = 5x + 30

-30 = 5x - 6y ⇒ 5x - 6y = -30

Now let's look at the inequality symbol: The shaded area is below so it will be a less than symbol and it is a solid line so the equal sign is included.

Answer: 5x - 6y ≤ -30