Question

Can someone please correctly answer and show their work on problems 21 and 22? This is algebra 2 by the way.

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Answer 1

21)
`\( x + y \geq 1 \)`:

Graph the line
`\(x + y = 1\)`, shading above. Represents points satisfying
`\(x + y\)` greater than or equal to 1.

22)
`\( y < -9x + 4 \)`:

Graph the line
`\(y = -9x + 4\)`, shading below. Represents points where
`\(y\)`is less than -9 times
`\(x\)` plus 4.

To sketch the graphs of the linear inequalities, we'll start by finding the boundary lines (equality lines) and then determine the shaded region based on the inequality.

**21)
`\( x + y \geq 1 \):`**

First, find the boundary line by setting
`\( x + y = 1 \)` and graph it. This line passes through points (1,0) and (0,1).

The inequality includes points above and on the line, so shade the region above the line.

**Graph for
`\( x + y \geq 1 \):`**

(Attachment 1)

**22)
`\( y < -9x + 4 \):`**

Find the boundary line by setting
`\( y = -9x + 4 \)` and graph it. This line has a slope of -9 and a y-intercept of 4.

The inequality includes points below the line, so shade the region below the line.

**Graph for
`\( y < -9x + 4 \)`:**

(Attachment 2)

These sketches represent the graphs of the given linear inequalities. The shaded regions indicate the solutions to the inequalities.