To determine the equation of a trend line in slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we need to identify the correct option based on the slope and intercept values.
From the options given:
- \( y = -14x \)
- \( y = -\frac{1}{4}x \)
- \( y = 1x + 9 \)
- \( y = 1x + 9 \) (duplicate)
- \( y = -14x + 9 \)
- \( y = -\frac{1}{4}x + 9 \)
- \( y = -58x + 9 \)
For the equation to be in slope-intercept form, the coefficient of \( x \) represents the slope and the constant represents the y-intercept. Out of the options provided, we can identify the following:
- If the slope is negative or positive, that will dictate the direction of the line.
- The presence of "+ 9" indicates that the line crosses the y-axis at the point (0, 9).
Without additional context regarding the data points or slope required, the possible trend lines presented are valid depending on the specific data they relate to.
If we specifically want a trend line that typically reflects a downward trend with the "y-intercept of 9", then the best choice would be either \( y = -14x + 9 \) or \( y = -\frac{1}{4}x + 9 \).
However, without further analysis or data, the most accurate answer cannot be conclusively determined.
If you have particular data for creating a trend line, a dataset reflecting trends would help in identifying the correct slope and intercept accurately.