Question

1. -x + y ≤ -1

to the teacher:
for online: this assessment contains question(s) using the drawing tool. you may want to re
use of the drawing tool with your students prior to taking the test. an example question is giv
abeka sample test.
for the pdf: this assessment contains question(s) involving graphing. you may want to edit
directions for that section since they currently apply to using the drawing tool in the online te
shade the correct region on the graph for the inequality. click the paintbrush button below the pl
use the tools to shade. click the green check mark to save your work.
close
(graph with x-axis from -5 to 5 and y-axis, line plotted, scroll down to see more)

Explanation:

Step1: Rewrite the inequality

Rewrite \(-x + y \leq -1\) as \(y \leq x - 1\). This is in slope - intercept form (\(y=mx + b\)), where the slope \(m = 1\) and the y - intercept \(b=-1\).

Step2: Graph the boundary line

The boundary line is \(y=x - 1\). Since the inequality is \(\leq\), the line should be a solid line (because the points on the line are included in the solution set). We can find two points on the line: when \(x = 0\), \(y=-1\); when \(x = 1\), \(y=1 - 1=0\). Plot these points \((0,-1)\) and \((1,0)\) and draw a solid line through them.

Step3: Determine the shading region

To determine which side of the line to shade, we can use a test point. A common test point is \((0,0)\). Substitute \(x = 0\) and \(y = 0\) into the inequality \(y\leq x - 1\): \(0\leq0 - 1\), which simplifies to \(0\leq - 1\). This is false. So we shade the region that does not contain the test point \((0,0)\). In other words, we shade the region below the line \(y=x - 1\) (since the test point above the line gave a false statement, we shade the opposite side).

Answer:

To graph the inequality \(-x + y\leq - 1\) (or \(y\leq x - 1\)):

1. Draw a solid line through the points \((0,-1)\) and \((1,0)\) (since the inequality is \(\leq\), the line is solid).
2. Shade the region below the line (the region that does not contain the point \((0,0)\)).