Question
Which graph best represents: y = -4(x+3) -2
Answers
GPT-4o mini
To analyze the equation \( y = -4(x + 3) - 2 \), we can rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
1. Distribute the -4:
\[
y = -4x - 12 - 2
\]
2. Combine like terms:
\[
y = -4x - 14
\]
From this, we can see:
- The slope \( m \) is -4, which indicates that the line will descend steeply as we move to the right.
- The y-intercept \( b \) is -14, meaning that the line crosses the y-axis at the point (0, -14).
To graph this equation:
- Start at the y-intercept (0, -14) on the graph.
- From this point, use the slope of -4 to find another point. The slope -4 can be interpreted as "down 4 units over 1 unit to the right." So, starting from (0, -14), move down to (1, -18).
The line will continue in this fashion, sloping downwards.
You would look for a graph that shows a line that:
- Has a steep negative slope.
- Crosses the y-axis at -14.
If you're given specific graph options to choose from, you would select the one that closely aligns with these characteristics.
1. Distribute the -4:
\[
y = -4x - 12 - 2
\]
2. Combine like terms:
\[
y = -4x - 14
\]
From this, we can see:
- The slope \( m \) is -4, which indicates that the line will descend steeply as we move to the right.
- The y-intercept \( b \) is -14, meaning that the line crosses the y-axis at the point (0, -14).
To graph this equation:
- Start at the y-intercept (0, -14) on the graph.
- From this point, use the slope of -4 to find another point. The slope -4 can be interpreted as "down 4 units over 1 unit to the right." So, starting from (0, -14), move down to (1, -18).
The line will continue in this fashion, sloping downwards.
You would look for a graph that shows a line that:
- Has a steep negative slope.
- Crosses the y-axis at -14.
If you're given specific graph options to choose from, you would select the one that closely aligns with these characteristics.