To write an equation in slope-intercept form \(y = mx + b\), we first need to identify the slope (m) and the y-intercept (b) from the given data points.
The data points provided in the table appear to be:
\[ \begin{align*} 1 & \to 0 \ -5 & \to 3 \ -11 & \to 3 \ -17 & \to 9 \ \end{align*} \]
Noticing that the x-values seem to be in the pattern of \(x = 0, 3, 3, 9\) and y-values \(y = 1, -5, -11, -17\).
However, let’s summarize it as follows from the corrected table:
\[ \begin{align*} (0, -1) \ (3, -5) \ (3, -11) \ (9, -17) \ \end{align*} \]
We can use the first two points \( (0, -1) \) and \( (3, -5) \) to calculate the slope.
- Calculate the Slope \(m\):
The slope \(m\) is calculated as follows:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-1)}{3 - 0} = \frac{-5 + 1}{3} = \frac{-4}{3} = -\frac{4}{3} \]
- Find the y-intercept \(b\):
Since we have the point (0, -1), we can see that when \(x = 0\), \(y = -1\). Therefore, the y-intercept \(b\) is \(-1\).
- Write the Equation:
Now that we have \(m\) and \(b\), we can write the equation in slope-intercept form:
\[ y = -\frac{4}{3}x - 1 \]
This is the equation that represents the relationship between \(x\) and \(y\) based on the points from the table.
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