Questions: y < 2x + 4 y <= -(1/2)x - 3 Which graph represents the system of inequalities?

Solution Steps

The first inequality is \(y < 2x + 4\). The line will have a slope of 2 and a y-intercept of 4. It will be a dashed line since it's a strict inequality (\(< \)). The shading will be below the line because \(y\) is _less than_ the expression.

The second inequality is \(y \le -\frac{1}{2}x - 3\). The line will have a slope of \(-\frac{1}{2}\) and a y-intercept of -3. It will be a solid line because it's a less than or equal to inequality (\(\le \)). The shading will be below the line because \(y\) is _less than or equal to_ the expression.

We are looking for a graph with a dashed line with slope 2 and y-intercept 4, and a solid line with slope \(-\frac{1}{2}\) and y-intercept -3. Both inequalities are shaded below their respective lines, so the overlapping shaded region will be where both conditions are true. The only graph that matches these criteria is graph X.

Final Answer