Question
Which graph best represents `y=-4\left(x+3\right)-2?`
Answers
GPT-4o mini
To analyze the equation \( y = -4(x + 3) - 2 \), let's first simplify it into slope-intercept form, \( y = mx + b \).
1. Distribute the -4:
\[
y = -4x - 12 - 2
\]
2. Combine like terms:
\[
y = -4x - 14
\]
Now we have a linear equation in the form \( y = mx + b \), where the slope \( m = -4 \) and the y-intercept \( b = -14 \).
To graph this equation, we can follow these steps:
1. **Plot the y-intercept**: The y-intercept is the point where the graph crosses the y-axis, which occurs at \( (0, -14) \).
2. **Use the slope to find another point**: The slope is -4, which means that for every 1 unit you move to the right (increasing \( x \)), you move 4 units down (decreasing \( y \)). Starting from the y-intercept at \( (0, -14) \):
- Moving 1 unit to the right: \( (1, -14) \)
- Moving down 4 units: \( (1, -14 - 4) = (1, -18) \)
3. **Plot the second point**: Plot the point \( (1, -18) \).
4. **Draw the line**: Connect the two points with a straight line extending in both directions.
Using this information, you can plot the graph of the equation \( y = -4(x + 3) - 2 \).
If you are provided with specific options for graphs, look for the graph that has a negative slope and passes through the point \( (0, -14) \) and the general downward trend corresponding to the slope of -4.
1. Distribute the -4:
\[
y = -4x - 12 - 2
\]
2. Combine like terms:
\[
y = -4x - 14
\]
Now we have a linear equation in the form \( y = mx + b \), where the slope \( m = -4 \) and the y-intercept \( b = -14 \).
To graph this equation, we can follow these steps:
1. **Plot the y-intercept**: The y-intercept is the point where the graph crosses the y-axis, which occurs at \( (0, -14) \).
2. **Use the slope to find another point**: The slope is -4, which means that for every 1 unit you move to the right (increasing \( x \)), you move 4 units down (decreasing \( y \)). Starting from the y-intercept at \( (0, -14) \):
- Moving 1 unit to the right: \( (1, -14) \)
- Moving down 4 units: \( (1, -14 - 4) = (1, -18) \)
3. **Plot the second point**: Plot the point \( (1, -18) \).
4. **Draw the line**: Connect the two points with a straight line extending in both directions.
Using this information, you can plot the graph of the equation \( y = -4(x + 3) - 2 \).
If you are provided with specific options for graphs, look for the graph that has a negative slope and passes through the point \( (0, -14) \) and the general downward trend corresponding to the slope of -4.