Complete the point-slope equation of the line through (-2,6) and (1,1). Use exact numbers. y-6=

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Complete the point-slope equation of the line through  (-2,6) and  (1,1). Use exact numbers.  y-6=

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Calculate Slope: First, we need to find the slope of the line that passes through the points (-2,6) and (1,1). The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Let's calculate the slope: m = (1 - 6) / (1 - (-2)) m = (-5) / (3) m = -5/3Use 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 (-2,6) for this example. So, substituting the slope and the coordinates of the point into the point-slope form, we get: y - 6 = (-5/3)(x - (-2))Simplify Equation: Simplify the equation by distributing the slope on the right side: y - 6 = (-5/3)(x + 2) y - 6 = (-5/3)x - (5/3)(2) y - 6 = (-5/3)x - 10/3Check Equation: Now, we have the point-slope form of the equation of the line. However, we can check if the equation is correct by substituting the coordinates of the other point (1,1) into the equation to see if it satisfies the equation. Substitute x = 1 and y = 1 into the equation: 1 - 6 = (-5/3)(1) - 10/3 -5 = (-5/3) - 10/3 -5 = -15/3 -5 = -5 The equation is satisfied, so there is no math error.

Complete the point-slope equation of the line through $(-2,6)$ and $(1,1)$ . Use exact numbers. $\newline$ $y-6=$

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Complete the point-slope equation of the line through $(-2,6)$ and $(1,1)$ . Use exact numbers. $\newline$ $y-6=$