To fill in the blanks, we first need to analyze the given data points (X, Y):
- When \(X = 1\), \(Y = -12\)
- When \(X = 2\), \(Y = -15\)
- When \(X = 3\), \(Y = -18\)
- When \(X = 4\), \(Y = -21\)
To calculate the slope (Blank 1):
The slope \(m\) can be calculated using the formula: \[ m = \frac{Y_2 - Y_1}{X_2 - X_1} \] Using two points, for instance, (1, -12) and (2, -15): \[ m = \frac{-15 - (-12)}{2 - 1} = \frac{-15 + 12}{1} = \frac{-3}{1} = -3 \]
So, the slope function is C -3.
To calculate the y-intercept (Blanks 2 and 3):
Using the slope-intercept form of the line, \(Y = mX + b\), we can rearrange it to find \(b\) (the y-intercept) using one of the points. Let's use (1, -12): \[ -12 = -3(1) + b \] \[ -12 = -3 + b \] \[ b = -12 + 3 = -9 \]
This means the y-intercept is \(b = -9\).
So, we need to choose options for Blank 2 and Blank 3. Since we have established that the y-intercept is \(y = -9\):
- Blank 2 can be inferred as B 0 (for the y-intercept in the context of graphing being a point on the Y-axis).
- Blank 3 can be inferred as C -9 (the actual value of the y-intercept).
Putting it all together:
- Blank 1: C -3
- Blank 2: B 0
- Blank 3: C -9
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