Answer:
[tex]y\geq 5x+3\\y < x-1[/tex]
Step-by-step explanation:
The red dashed line is linear and intercepts the y-axis below the x-axis. The slope of the line is 1, and the intercept point is at y=-1 which makes its equation y = 1*x-1.
The blue line is also linear and has increases by 5 units for every unit increment of x, giving it the slope 5. The line intercepts the y-axis at y = 3, giving it the equation y = 5x + 3.
Now the shaded area lies between these two lines in the bottom left quadrant. Note that the y-values in the shaded area are always smaller compared to the y-value of the red line for the same values of x. This is because the shaded area lies below the red line.
Contrary to this the y-values in the shaded area are always larger than (or equal to) the y-values of the blue line for the same values of x. This is because if you were to enlarge the graph, the shaded area would always be above or on the blue line. This leads us to write the inequality as,
[tex]y\geq 5x+3\\y < x-1[/tex]
Which matches the second option.
