To write the equation of the trend line in slope-intercept form \(y = mx + b\), we need to determine the slope \(m\) and the y-intercept \(b\).
From the points provided, we can identify two points on the trend line, for example, the points \((0, 8)\) and \((40, 0)\).
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Finding the slope \(m\): The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \((0, 8)\) and \((40, 0)\): \[ m = \frac{0 - 8}{40 - 0} = \frac{-8}{40} = -\frac{1}{5} \]
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Finding the y-intercept \(b\): The y-intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0, 8)\), we see that: \[ b = 8 \]
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Writing the equation: Substituting \(m\) and \(b\) into the slope-intercept form: \[ y = -\frac{1}{5}x + 8 \]
Now we compare this with the provided options.
The correct equation is: \[ y = -\frac{1}{5}x + 8 \] This matches the option:
- \(y = -15x + 8\) (the slope should be \(-\frac{1}{5}\), not \(-15\)).
There seems to be a mistake in the option's representation. The correct slope should indicate the \( -\frac{1}{5} \) rather than saying \(-15\), which is not adequate.
Therefore, based on the accurate calculations, the final correct answer for the slope-intercept form, based on the options provided, is: None of the options are correct. The right equation based on our calculation is \(y = -\frac{1}{5}x + 8\).