Questions: 1. The graph of which inequality is shown in the accompanying diagram? A. x-y>2 B. x+y>2 C. x-y<2 D. x+y<2
Transcript text: 1. The graph of which inequality is shown in the accompanying diagram?
A. $x-y>2$
B. $x+y>2$
C. $x-y<2$
D. $x+y<2$
Solution
Solution Steps
Step 1: Find the equation of the line.
The line passes through the points (2, 0) and (0, -2). The slope is (-2 - 0) / (0 - 2) = -2/-2 = 1. Using the point-slope form with the point (2,0), we get: y - 0 = 1(x - 2), which simplifies to y = x - 2.
Step 2: Determine the inequality sign.
The shaded region is _below_ the line, indicating "less than." Since the line is dashed, it doesn't include points on the line itself, so the inequality must be "less than," not "less than or equal to." This gives us y < x - 2.
Step 3: Rewrite the inequality in the standard form.
Subtracting x from both sides of y < x - 2 gives us -x + y < -2. Multiplying both sides by -1 and reversing the inequality sign yields x - y > 2.