which linear equality will not have a shared solution set with the graphed linear inequality?\n$y>\frac{2}{5}…

Explanation:

Step1: Analyze the slope and y - intercept of the given inequality

The given inequality is $y\geq-\frac{5}{2}x - 3$. Its slope $m_1=-\frac{5}{2}$ and y - intercept $b_1=-3$.

Step2: Analyze each option

Option 1: $y>\frac{2}{5}x + 2$

The slope $m_2=\frac{2}{5}$. Since the slopes $m_1\neq m_2$, the lines are not parallel and will intersect, so there will be a shared solution.

Option 2: $y<-\frac{5}{2}x - 7$

The slope $m_3 =-\frac{5}{2}$, same as the given inequality's slope. The y - intercept $b_3=-7$. The given inequality is $y\geq-\frac{5}{2}x - 3$. The region of $y<-\frac{5}{2}x - 7$ is below the line $y =-\frac{5}{2}x - 7$ and the region of $y\geq-\frac{5}{2}x - 3$ is above the line $y=-\frac{5}{2}x - 3$. These two regions do not overlap.

Option 3: $y>-\frac{2}{5}x - 5$

The slope $m_4=-\frac{2}{5}$. Since $m_1\neq m_4$, the lines are not parallel and will intersect, so there will be a shared solution.

Option 4: $y<\frac{5}{2}x + 2$

The slope $m_5=\frac{5}{2}$. Since $m_1\neq m_5$, the lines are not parallel and will intersect, so there will be a shared solution.

Answer:

$y<-\frac{5}{2}x - 7$