10. look for relationships which inequality, $y > \\frac{3}{4}x - 2$ or $3x - 4y < 8$, is shown by the…

Explanation:

Step1: Rewrite second inequality to slope-intercept form

Start with $3x - 4y < 8$. Subtract $3x$ from both sides: $-4y < -3x + 8$ Divide by $-4$ (reverse inequality sign): $y > \frac{3}{4}x - 2$

Step2: Test a point in the shaded region

Choose the origin $(0,0)$ (in the shaded area). Substitute into $y > \frac{3}{4}x - 2$: $0 > \frac{3}{4}(0) - 2$ $0 > -2$, which is true.

Step3: Verify the boundary line

Both inequalities correspond to the dashed line $y = \frac{3}{4}x - 2$ (dashed for strict inequality), which matches the graph.

Answer:

Both inequalities are equivalent, and the graph shows $y > \frac{3}{4}x - 2$ (or $3x - 4y < 8$, since they are algebraically the same). The dashed boundary line $y = \frac{3}{4}x - 2$ and the shaded region above the line (verified by testing $(0,0)$) confirm this, as substituting the point into either inequality gives a true statement.