Question

part c
graph the linear inequality.

1. ( y leq \frac { 1 } { 4 } x - 2 )

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

Explanation:

Step1: Identify the slope and y - intercept

The given inequality is in the form \(y\leq mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the inequality \(y\leq\frac{1}{4}x-2\), by comparing with the slope - intercept form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept of the line \(y=mx + b\)), we can directly read off the values.

Step2: Determine the type of line

Since the inequality is \(y\leq\frac{1}{4}x - 2\) (the symbol is \(\leq\), which includes equality), the line \(y=\frac{1}{4}x-2\) should be a solid line.

Step3: Determine the shaded region

Since \(y\leq\frac{1}{4}x - 2\), we shade the region below the line \(y=\frac{1}{4}x-2\).

Answer:

\(m = \frac{1}{4}\), \(b=-2\), circle “solid line”, shade “below”.