To graph the inequality [tex]\( y - 5 > 2x - 10 \)[/tex], let's break down the steps:
1. Rewrite the Inequality:
First, we'll rewrite the inequality in slope-intercept form (i.e., [tex]\( y = mx + b \)[/tex]). Starting with the given inequality:
[tex]\[
y - 5 > 2x - 10
\][/tex]
2. Isolate [tex]\( y \)[/tex]:
Add 5 to both sides to isolate [tex]\( y \)[/tex]:
[tex]\[
y - 5 + 5 > 2x - 10 + 5
\][/tex]
[tex]\[
y > 2x - 5
\][/tex]
3. Determine the Boundary Line:
The boundary line for this inequality is [tex]\( y = 2x - 5 \)[/tex]. We will draw this line, but since the inequality is strict (">" rather than "≥"), the boundary line will be dashed to indicate that points on the line are not included in the solution.
4. Graph the Boundary Line:
- The slope ([tex]\( m \)[/tex]) is 2, indicating that for every 1 unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] increases by 2 units.
- The y-intercept ([tex]\( b \)[/tex]) is -5, indicating that the line crosses the y-axis at [tex]\( (0, -5) \)[/tex].
Draw the line [tex]\( y = 2x - 5 \)[/tex], making sure to use a dashed line.
5. Shade the Region:
Since the inequality is [tex]\( y > 2x - 5 \)[/tex], we need to shade the region above the dashed line. This is because for [tex]\( y \)[/tex] to be greater than [tex]\( 2x - 5 \)[/tex], any point (x, y) satisfying the inequality will lie above the boundary line.
6. Determine the Matching Graph:
Among the given choices (A, B, C, and D), we need to find the graph that has:
- A dashed boundary line passing through the points (0, -5) and with a slope of 2.
- The region above the dashed line shaded.
Considering the steps above:
- The line has a slope of 2.
- The y-intercept is -5.
- The line is dashed.
- The area above the line is shaded.
The correct graph that matches these criteria should be identified based on the given choices.
We conclude that the correct answer is:
```
commented_graph_choice_number
```
