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sammy [17]
3 years ago
14

PLEASE HELP BRAINLY - which option is correct?

Mathematics
1 answer:
LuckyWell [14K]3 years ago
7 0

Answer:

y > \frac{2x}{3} + 1

Step-by-step explanation:

Given:

The graph in the attachment where the coordinates are (3,3) and (-3,-1)

Required:

Which inequality represent the graph

The first step is to determine the slope of the graph

m = \frac{y_2 - y_1}{x_2 - x_1}

Where m represents the slope, (x_1, y_1) = (3,3) and (x_2, y_2) = (-3,-1)

m = \frac{-1 - 3}{-3 - 3}

m = \frac{-4}{-6}

Simplify to lowest term

m = \frac{2}{3}

Next is to determine the equation of the line using the slope formula

m = \frac{y - y_1}{x - x_1}, (x_1, y_1) = (3,3)  and m = \frac{2}{3}

\frac{2}{3} = \frac{y - 3}{x - 3}

Cross multiply

2 * (x - 3) = 3 * (y - 3)

Open both brackets

2 x - 6 = 3y -9

Collect like terms

2 x - 6 +9= 3y

2 x+3= 3y

Divide through by 3

\frac{2x}{3} + \frac{3}{3} = \frac{3y}{3}

\frac{2x}{3} + 1 = y

Reorder

y = \frac{2x}{3} + 1

Next is to determine the inequality sign

  • The dotted lines on the graph shows that the inequality sign is either > or <
  • Since the shaded region is the upper part of the graph, then the > inequality sign will be considered,

The inequality becomes

y > \frac{2x}{3} + 1

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