To analyze the linear function with an x-intercept of 12 and a slope of \(\frac{3}{8}\), we first need to determine its equation in slope-intercept form, \(y = mx + b\).
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Finding the y-intercept: The x-intercept is the point where \(y = 0\). So, when \(x = 12\): \[ 0 = \frac{3}{8}(12) + b \] \[ 0 = \frac{36}{8} + b \] \[ 0 = \frac{9}{2} + b \] \[ b = -\frac{9}{2} \]
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Equation of the function: The equation of the linear function is: \[ y = \frac{3}{8}x - \frac{9}{2} \]
Next, we look at the table you provided to find the slope and y-intercept of the linear function represented by this table.
To find the slope from the points in the table, let's find two points to calculate the slope \(m\). The points must be determined from the table provided; however, it's not clear from your message what these points are as they are written in fractions.
If we assume that the values are from the table provided in order, let's say:
- \(x_1 = -\frac{2}{3}\), \(y_1 = -\frac{3}{4}\)
- \(x_2 = -\frac{1}{6}\), \(y_2 = \text{some y-value}\)
The slope \(m\) can be found by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
You can perform this calculation with the actual values given in the table to find the slope of the linear function represented by the table.
Now, once you have found the slope and y-intercept of the function represented by the table, you can compare:
- If the slope of the function from the table equals \(\frac{3}{8}\), then both functions have the same slope.
- If the y-intercept of the function from the table equals \(-\frac{9}{2}\), then both functions have the same y-intercept.
Based on the results of your calculations, you can select one of the provided options:
- It has the same slope and the same y-intercept.
- It has the same slope and a different y-intercept.
- It has the same y-intercept and a different slope.
- It has a different slope and a different y-intercept.
Please find the slope and y-intercept from the table to finalize which option is correct.