To determine which answer matches the given equation [tex]\( y = -3x - 2 \)[/tex], we need to graph the line and analyze its key characteristics.
### Step-by-Step Solution:
1. Identify the slope and y-intercept from the equation:
- The equation of the line is in the slope-intercept form [tex]\( y = mx + b \)[/tex].
- Here, [tex]\( m \)[/tex] (the slope) is [tex]\(-3\)[/tex].
- The y-intercept [tex]\( b \)[/tex] is [tex]\(-2\)[/tex].
2. Plot the y-intercept:
- The y-intercept is the point where the line crosses the y-axis (when [tex]\( x = 0 \)[/tex]).
- For [tex]\( y = -3(0) - 2 \)[/tex]:
[tex]\[
y = -2
\][/tex]
- Plot the point [tex]\( (0, -2) \)[/tex] on the graph.
3. Determine another point on the line using the slope:
- The slope is [tex]\(-3\)[/tex], meaning the line goes down 3 units vertically for every 1 unit it moves to the right horizontally.
- Starting from the y-intercept [tex]\( (0, -2) \)[/tex], move 1 unit to the right ([tex]\( x = 1 \)[/tex]) and 3 units down ([tex]\( y = -5 \)[/tex]):
[tex]\[
x = 1, \quad y = -3(1) - 2 = -3 - 2 = -5
\][/tex]
- Plot the point [tex]\( (1, -5) \)[/tex] on the graph.
4. Draw the line:
- Using a ruler, draw a line through the points [tex]\( (0, -2) \)[/tex] and [tex]\( (1, -5) \)[/tex].
- Extend the line in both directions.
5. Compare with the given answer choices:
- We need to see which of the given options (A, B, C, D) matches the graph we drew.
### Summary of Key Points on the Graph:
- The line has a negative slope and is steep, decreasing 3 units vertically for each 1 unit it moves horizontally.
- The line crosses the y-axis at the point [tex]\( (0, -2) \)[/tex] and the point [tex]\( (1, -5) \)[/tex] lies on the line.
### Conclusion:
Upon comparing the graphs in the given answer choices with the one we drew, we select the one that matches these characteristics - which is the line with a y-intercept of [tex]\(-2\)[/tex] and a downward slope of [tex]\(-3\)[/tex].
In this case, the answer that matches the graph drawn is the correct one. Ensure that the characteristics (steepness and crossing points) are visually identical.
If you have access to visual depictions of these graphs (choices A, B, C, D), please match them accordingly to identify the correct answer.
