Question

57.3 mini quiz: graphing linear inequalities

1. circle all the terms that best describe the line type and shading of >

solid line dashed line shade above shade below

1. circle all the terms that best describe the line type and shading of ≤

solid line dashed line shade above shade below

1. circle the best choices for the following statement.

when you graph ( y<\frac{2}{3}x - 5 ), the line will be solid or dashed and shaded above or below

1. shade the appropriate side of the graph for the following inequalities.

a) ( yleq\frac{3}{4}x - 2 ) b) ( x>3 )

1. graph and shade the following.

a) ( y<2x + 3 ) b) ( ygeq-\frac{5}{2}x - 1 )

Explanation:

1. For inequalities with \(>\) (not including the line), the line is dashed. And since \(y > \text{(expression)}\), we shade above the line.
2. For inequalities with \(\leq\) (including the line), the line is solid. And since \(y\leq\text{(expression)}\), we shade below the line.
3. For \(y <\frac{2}{3}x - 5\), since it's \(<\) (not including the line), the line is dashed. And since \(y <\text{(expression)}\), we shade below the line.

4.

• a) For \(y\leq\frac{3}{4}x - 2\), since it's \(\leq\) (including the line), we shade the region below the line.
• b) For \(x > 3\), since it's \(>\) (not including the line \(x = 3\), a vertical line), we shade the region to the right of \(x = 3\).

5.

• a) For \(y < 2x+3\), draw the dashed line \(y = 2x + 3\) (using slope - intercept form \(y=mx + b\), \(m = 2\), \(b=3\)) and shade below the line.
• b) For \(y\geq-\frac{5}{2}x-1\), draw the solid line \(y=-\frac{5}{2}x - 1\) ( \(m=-\frac{5}{2}\), \(b =- 1\)) and shade above the line.

Answer:

1. Dashed Line, Shade Above
2. Solid Line, Shade Below
3. Dashed, Shade Below

4.

• a) Shade below \(y=\frac{3}{4}x - 2\)
• b) Shade to the right of \(x = 3\)

5.

• a) Draw dashed \(y = 2x+3\), shade below
• b) Draw solid \(y=-\frac{5}{2}x - 1\), shade above