Question

A graph is shown below:

solid line joining ordered pair 0, negative 2 and 1, 3 and the region below this line is shaded

Which of the following inequalities is best represented by this graph?
5x + y ≤ 2
5x + y ≥ 2
5x − y ≤ 2
5x − y ≥ 2

Answer 1

I think the answer is C

Answer 2

Answer: Hello mate!

You can see that the solid line passes through the points (0, -2) and (1, 3)

So we can find the slope of the solid line using the next relation:

For two points (x1,y1) and (x2,y2), the slope is calculated as:

`s = (y2 - y1)/(x2 - x1)`

Then, the slope between the points that we have is:

`s = (3 -(-2))/(1-0) = 5`

this means that the equation of the line is: y = 5x + b

where b is the y-intercept, and we already know that the y is equal to -2 when x is equal to 0, so the y-intercept is equal to -2.

And the equation of the solid line is: y = 5x - 2

notice that the shaded area is at the right of the area; so we have:

y ≥ 5x - 2

y - 5x ≥ -2

now we multiply both sides by -1, which also changes the direction of the relation:

5x - y ≤ 2

then the right option is the second one.