Questions: Plot two points on the boundary line of the graph of the line x, y=1, 1

Solution Steps

The given inequality is \( y \leq -2x + \frac{1}{2} \).

To plot the boundary line, convert the inequality to an equation: \[ y = -2x + \frac{1}{2} \]

To plot the line, we need two points. Let's find the points by choosing values for \( x \) and solving for \( y \).

1. When \( x = 0 \): \[ y = -2(0) + \frac{1}{2} = \frac{1}{2} \] So, one point is \( (0, \frac{1}{2}) \).

2. When \( x = 1 \): \[ y = -2(1) + \frac{1}{2} = -2 + \frac{1}{2} = -\frac{3}{2} \] So, another point is \( (1, -\frac{3}{2}) \).

Final Answer