To find the equation of the linear function based on the points provided, we first need to identify the coordinates of the two points you've given:
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Point 1: \(Y (12, 11)\) → This appears to be written incorrectly as this should be two separate points. Assuming you meant:
- Point A: (12, Y)
- Point B: (11, Y)
But we will interpret "Y 12, 11" as points in the graph which should be
- Point A: \((-3, 11)\)
- Point B: \((-4, 12)\)
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Point 2: \(X (-3, -4)\) → Let's assume this also represents the x-coordinates for the points we are considering.
Given the assumed points (-3, 11) and (-4, 12), we can find the slope (m) of the linear function using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the points in, we have: \[ m = \frac{12 - 11}{-4 - (-3)} = \frac{1}{-1} = -1 \]
Next, we can use the point-slope form of the equation of a line, which is:
\[ y - y_1 = m(x - x_1) \]
Using Point A \((-3, 11)\): \[ y - 11 = -1(x + 3) \]
Expanding this gives: \[ y - 11 = -x - 3 \] \[ y = -x + 8 \]
Thus, the equation of the line represented by the points (-3, 11) and (-4, 12) is:
\[ y = -x + 8 \]
If the points given were interpreted differently, please clarify the points, and I can help you find the correct linear equation.