Which system of linear inequalities is represented by the graph?

x + 3y > 6

y ≥ 2x + 4

the correct option is D.

Step-by-step explanation:

x+3y>6

y≥2x+4

consider the equation x+3y=6

3y = 6-x

this line is in the form of y = mx + c

where m is the slope os the line and c is the y intercept of the line

therefore the line has a y intercept of 2  and slope of-1/3

therefore the line has negative slope with positive intercept.

now consider the line y=2x+4

this line is in the form of y = mx + c

where m is the slope os the line and c is the y intercept of the line

therefore slope = 2 and y intercept = 4

therefore the line has positive slope and positive y intercept.

in option a both line has positive intercept so it cant be an answer.

in option b one line has positive intercept of 2 and another with negative intercept of -4 but we need intercept of both line to be positive so it cant be an answer.

in option c both line has negative intercept of -2 and -4 but we need intercept of both line to be positive so it cant be an answer.

in option d both line has positive intercept of 2 and 4 and also one of the line has negative slope and another line has positive slope so it should be an answer

further to confirm consider x+3y>6

put the point 0,0 in the inequality

0>6 which is wrong so 0,0 cant lie in the region which is true according to the graph.

is means division by fractions

step-by-step explanation: