To determine the solution set for the given graph of an inequality, we analyze the characteristics described:
- The dashed line indicates that the inequality does not include the line itself, which suggests that "<" or ">" is used (not "≤" or "≥").
- Since the area above the dashed line is shaded, this suggests that the inequality is "greater than" the linear equation represented by the dashed line.
The y-intercept is at \( (0, -2.5) \), and the x-intercept is approximately at \( (1.5, 0) \). We can find the slope of the line by calculating the change in y over the change in x using these intercepts.
The slope \( m \) can be calculated as follows: \[ m = \frac{0 - (-2.5)}{1.5 - 0} = \frac{2.5}{1.5} \approx \frac{5}{3} \]
Now we can write the equation of the line in slope-intercept form: \[ y = \frac{5}{3}x - 2.5 \]
To express the inequality, since the area above the line is shaded, we can say: \[ y > \frac{5}{3}x - 2.5 \]
To match it with one of the provided options, we can convert \( \frac{5}{3}x - 2.5 \) into the form of \( 2x - y < 3 \):
\[ y < 2x - 3 \] rearranging gives: \[ 2x - y > 3 \]
Thus, amongst the provided options, the correct inequality that describes the shaded area above the line is: \( 2x - y < 3 \).
Final response: 2x−y<3