Question

1. y < -\frac{2}{3}x + 3

m=
b=
circle one:
dashed / solid line
shade above / below

Explanation:

Step1: Identify the slope - intercept form

The inequality is \(y<-\frac{2}{3}x + 3\). The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.

Step2: Determine the slope \(m\)

Comparing \(y<-\frac{2}{3}x + 3\) with \(y = mx + b\), we get \(m=-\frac{2}{3}\).

Step3: Determine the \(y\) - intercept \(b\)

Comparing \(y<-\frac{2}{3}x + 3\) with \(y = mx + b\), we get \(b = 3\).

Step4: Determine the line type

Since the inequality is \(y<-\frac{2}{3}x + 3\) (strict inequality), the line is dashed.

Step5: Determine the shading region

Since \(y<-\frac{2}{3}x + 3\), we shade below the line.

Answer:

\(m =-\frac{2}{3}\), \(b = 3\), circle dashed, shade below.