Question
What are the slopes of y=3x-4 and the table below
x|0|1|2|3|4
y|12|9|6|3|0
x|0|1|2|3|4
y|12|9|6|3|0
Answers
GPT-4o mini
To find the slope of the line represented by the equation \( y = 3x - 4 \), we can directly observe that it is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope. From this equation, the slope is \( 3 \).
Next, we can find the slope of the line represented by the table provided. To calculate the slope from the values in the table, we can use two points from the table. Let's take the points \( (0, 12) \) and \( (4, 0) \):
- The coordinates of the two points are:
- \( (x_1, y_1) = (0, 12) \)
- \( (x_2, y_2) = (4, 0) \)
The formula for the slope \( m \) between two points is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values we have:
\[
m = \frac{0 - 12}{4 - 0} = \frac{-12}{4} = -3
\]
So, the slope of the line represented by the table is \( -3 \).
To summarize:
- The slope of \( y = 3x - 4 \) is \( 3 \).
- The slope of the line represented by the table is \( -3 \).
Next, we can find the slope of the line represented by the table provided. To calculate the slope from the values in the table, we can use two points from the table. Let's take the points \( (0, 12) \) and \( (4, 0) \):
- The coordinates of the two points are:
- \( (x_1, y_1) = (0, 12) \)
- \( (x_2, y_2) = (4, 0) \)
The formula for the slope \( m \) between two points is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values we have:
\[
m = \frac{0 - 12}{4 - 0} = \frac{-12}{4} = -3
\]
So, the slope of the line represented by the table is \( -3 \).
To summarize:
- The slope of \( y = 3x - 4 \) is \( 3 \).
- The slope of the line represented by the table is \( -3 \).