Question

match the 5 graphs of linear inequalities with the correct symbolic form.
drag & drop the answer
$y > -4$
$y \geq -4$
$y \geq -2x + 5$
$x \geq -4$
$x > -4$
$y > \frac{1}{2}x + 4$
$y \leq -2x + 5$
$y < \frac{1}{2}x + 4$

Explanation:

Step1: Analyze the first (left) graph

The first graph (blue - shaded) is a horizontal line, and the shading is above or below? Wait, looking at the y - axis, the horizontal line seems to be at \(y=- 4\)? Wait, no, the first graph: the horizontal line, let's check the y - coordinate. Wait, the first graph (left - top) has a horizontal line, and the shading is above or below? Wait, the y - axis: the line is at \(y = - 4\)? Wait, no, the first graph (the blue one) has a horizontal line, and the shading is for \(y\geq - 4\) or \(y>-4\)? Wait, the line is solid or dashed? Wait, the first graph (blue) has a solid horizontal line? Wait, no, the first graph (left) is a horizontal line, and the shading is above? Wait, no, let's check the equations. The equation \(y\geq - 4\) or \(y > - 4\). Wait, the first graph (blue) has a horizontal line, and if the line is solid, then it's \(y\geq - 4\), if dashed, \(y>-4\). Looking at the graph, the first (blue) graph: the horizontal line, let's assume the line is \(y=-4\), and the shading is above (including the line), so the equation is \(y\geq - 4\).

Step2: Analyze the second (right) graph

The second graph (red - shaded) is a vertical line. The vertical line is at \(x=-4\), and the shading is to the right of the line. If the line is dashed, it's \(x > - 4\), if solid, \(x\geq - 4\). Looking at the graph, the red line is solid? Wait, no, the red graph: the vertical line, and the shading is to the right. So the equation is \(x\geq - 4\) (if solid) or \(x > - 4\) (if dashed). Wait, the options have \(x\geq - 4\) and \(x > - 4\).

Now, matching the graphs:

First (blue) graph: horizontal line, shading above, so \(y\geq - 4\) (since the line is solid? Wait, the first graph's line: looking at the grid, the horizontal line is at \(y = - 4\)? Wait, the first graph (blue) has a horizontal line, and the shading is for \(y\geq - 4\) (if solid) or \(y>-4\) (if dashed). The option \(y\geq - 4\) and \(y > - 4\) are present. Let's check the options: the first (blue) graph should match \(y\geq - 4\) (if the line is solid) or \(y > - 4\) (if dashed). The second (red) graph: vertical line at \(x=-4\), shading to the right, so \(x\geq - 4\) (if solid) or \(x > - 4\) (if dashed). The options have \(x\geq - 4\) and \(x > - 4\).

Wait, the first (blue) graph: let's check the equations. The first graph (blue) is horizontal, so \(y\) - related. The options for \(y\): \(y > - 4\), \(y\geq - 4\), \(y\geq - 2x + 5\), \(y < - 2x + 5\), \(y >\frac{1}{2}x + 4\), \(y <\frac{1}{2}x + 4\), \(y\leq - 2x + 5\). The horizontal line is \(y=-4\), so the equation is \(y\geq - 4\) (solid line) or \(y > - 4\) (dashed). The second (red) graph: vertical line \(x = - 4\), shading to the right, so \(x\geq - 4\) (solid) or \(x > - 4\) (dashed).

So the first (blue) graph matches \(y\geq - 4\), the second (red) graph matches \(x\geq - 4\).

Answer:

First (blue) graph: \(y\geq - 4\)

Second (red) graph: \(x\geq - 4\)