Question

PLEASE HELP BRAINLY - which option is correct?

Answer 1

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

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