Question

question 1 - 6
you have 2 hours to do homework tonight.

• you spend x hours on math.
• you spend y hours on science.

a graph shows the inequality: ( x + y leq 2 )
what does a point in the shaded area of the graph mean?
the point represents values for x and y which indicate that you spent more than 2 hours on homework
the point represents values for x and y which indicate that you finished your homework in 2 hours or less.
the point represents values for x and y which indicate that you did exactly 2 hours of math and 2 hours of science.
the point represents values for x and y which indicate that you did more than 4 hours of studying for both courses

Explanation:

Step1: Analyze the inequality

The inequality \(x + y\leq2\) means the sum of time spent on math (\(x\)) and science (\(y\)) is less than or equal to 2 hours.

Step2: Relate to the options

• For the first option: If \(x + y>2\), it would be outside the shaded area (since the inequality is \(x + y\leq2\)), so this option is wrong.
• For the second option: Since \(x + y\leq2\), it means the total time spent on both (math and science) homework is 2 hours or less. This matches the meaning of the inequality and the shaded area.
• For the third option: If \(x = 2\) and \(y=2\), then \(x + y=4>2\), which does not satisfy \(x + y\leq2\), so this option is wrong.
• For the fourth option: If \(x + y>4\), it is also not in line with \(x + y\leq2\), so this option is wrong.

Answer:

The point represents values for \(x\) and \(y\) which indicate that you finished your homework in 2 hours or less.