Question

Graph the inequality on the axes below.
x, minus, y, is less than, minus, 1
x−y<−1

were on the graph do i put the. points

Answer 1

To graph the inequality \( x - y < -1 \), you will first need to convert it into an equivalent equation to find the boundary line:

1. Rewrite the inequality as an equation:
\[
x - y = -1
\]

2. Next, solve for \( y \):
\[
y = x + 1
\]

This is the equation of a straight line with a slope of 1 and a y-intercept of 1.

### Step 1: Graph the Boundary Line
- Plot the y-intercept (0, 1) on the graph.
- Use the slope (1) to find another point: From (0, 1), move one unit up and one unit to the right to get to (1, 2).
- Draw a dashed line through these points because the inequality is strict (i.e., \( < \), not \( \leq \)).

### Step 2: Test a Point to Determine the Shading
You can choose a test point not on the line to determine where to shade. A common choice is the origin (0, 0).

Substituting \( (0, 0) \) into the inequality \( x - y < -1 \):
\[
0 - 0 < -1 \quad \text{(False)}
\]

Since the test point (0, 0) does not satisfy the inequality, shade the region that does not include the origin. This will be the area below the line \( y = x + 1 \).

### Summary
1. Draw a dashed line for \( y = x + 1 \).
2. Shade below this line to represent the solutions to the inequality \( x - y < -1 \).

You can also choose additional points to plot, such as when \( x = -2 \):
- When \( x = -2 \):
\[
y = -2 + 1 = -1 \quad \Rightarrow \quad (-2, -1) \text{ is on the line}
\]
Or when \( x = 0 \):
- When \( x = 0 \):
\[
y = 0 + 1 = 1 \quad \Rightarrow \quad (0, 1) \text{ is on the line}
\]

If you have graphing axes, you can plot these points accordingly and shade the appropriate region below the dashed line.