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:
[tex]s = \frac{y2 - y1}{x2 - x1}[/tex]
Then, the slope between the points that we have is:
[tex]s = \frac{3 -(-2)}{1-0} = 5[/tex]
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.
