Question

1. y ≥ x + 3

m=

b=

circle one:
dashed / solid line
shade above / below

Explanation:

Step1: Rewrite the inequality in slope - intercept form ($y = mx + b$)

Starting with \(3y\geq x + 3\). Divide each term by 3: \(y\geq\frac{1}{3}x + 1\).

Step2: Identify the slope ($m$) and y - intercept ($b$)

For the line \(y=\frac{1}{3}x + 1\), the slope \(m=\frac{1}{3}\) and the y - intercept \(b = 1\).

Step3: Determine the line type

Since the inequality is \(\geq\) (a non - strict inequality), the line is solid.

Step4: Determine the shading region

Since \(y\geq\frac{1}{3}x+1\), we shade above the line.

Answer:

\(m=\frac{1}{3}\), \(b = 1\), circle “solid line”, shade “above”.