Complete the point-slope equation of the line through (-1,6) and (1,5). Use exact numbers. y-6=◻

Calculate Slope: To find the point-slope form of the equation of a line, we first need to calculate the slope of the line using the two given points (-1,6) and (1,5). The slope (m) is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.Substitute Coordinates: Substitute the coordinates of the points into the slope formula: m = (5 - 6) / (1 - (-1)) = (-1) / (2) = -1/2.Apply Point-Slope Form: Now that we have the slope, we can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We can use either of the two points given, but let's use the point (-1,6).Final Equation: Substitute the slope and the coordinates of the point into the point-slope form: y - 6 = (-1/2)(x - (-1)) = (-1/2)(x + 1).

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Q. Complete the point-slope equation of the line through

(-1,6)

and

(1,5)

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Use exact numbers.

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y - 6 = \square

Calculate Slope: To find the point-slope form of the equation of a line, we first need to calculate the slope of the line using the two given points $(-1,6)$ and $(1,5)$ . The slope $m$ is given by the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.
Substitute Coordinates: Substitute the coordinates of the points into the slope formula: $m = \frac{5 - 6}{1 - (-1)} = \frac{-1}{2} = -\frac{1}{2}$ .
Apply Point-Slope Form: Now that we have the slope, we can use the point-slope form of the equation of a line, which is $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is a point on the line. We can use either of the two points given, but let's use the point $(-1,6)$ .
Final Equation: Substitute the slope and the coordinates of the point into the point-slope form: $y - 6 = \left(-\frac{1}{2}\right)(x - (-1)) = \left(-\frac{1}{2}\right)(x + 1)$ .