Question

look at the poster in your class
which inequality symbol is correct for the graph below

Explanation:

Step1: Determine the equation of the line

The line passes through \((0, 4)\) (y - intercept) and \((1.5, 0)\) (approximate x - intercept, or we can calculate the slope. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 4}{1.5-0}=-\frac{8}{3}\) (or we can see from the graph, the line has a slope of \(- 2\) approximately? Wait, let's take two points: \((0,4)\) and \((2,0)\), then slope \(m=\frac{0 - 4}{2-0}=- 2\). So the equation of the line is \(y=-2x + 4\) (using \(y=mx + b\), where \(m=-2\) and \(b = 4\)).

Step2: Check the inequality symbol

The line is solid (so the inequality is either \(\geq\) or \(\leq\)), and the shaded region is above the line (since when \(x = 0\), the shaded region includes \(y>4\)? Wait, no, let's test a point in the shaded region. Let's take \((0,5)\), which is in the shaded region. Plug into \(y\) and \(-2x + 4\): \(5\) and \(-2(0)+4 = 4\). So \(5\geq4\), so the inequality is \(y\geq - 2x+4\), so the inequality symbol related to the line (if we are writing the inequality for the graph) would involve \(\geq\) (since the line is solid and the region above is shaded, so the inequality is \(y\geq - 2x + 4\), so the symbol is \(\geq\)).

Answer:

\(\geq\)