Questions: Which linear equality will not have a shared solution set with the graphed linear inequality? y > 2/5 x + 2 y < -5/2 x - 7 y > -2/5 x - 5 y < 5/2 x + 2

Transcript text: Which linear equality will not have a shared solution set with the graphed linear inequality? $y>\frac{2}{5} x+2$ $y<-\frac{5}{2} x-7$ $y>-\frac{2}{5} x-5$ $y<\frac{5}{2} x+2$

Solution

Solution Steps

Step 1: Analyze the graph

The graphed inequality is $y \ge -\frac{5}{2}x - 3$. The line has a negative slope and a y-intercept of -3. The shaded region is above the line.

Step 2: Compare slopes and y-intercepts

The given options have different slopes and y-intercepts. We are looking for an inequality that does _not_ share any solutions with the graphed inequality.

Step 3: Identify non-overlapping solution sets

The inequality $y < \frac{5}{2}x + 2$ has a positive slope, and its shaded region will be below the line. Since the graphed inequality has a negative slope and the shaded region is above the line, these two inequalities represent opposite regions of the graph, and therefore they will not share any solutions.

Final Answer

$y < \frac{5}{2}x + 2$

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