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Complete the equation of the line through (-1,6) and (7,-2). Use exact numbers. y=

Complete the equation of the line through (−1,6) (-1,6) and (7,−2) (7,-2) .\newlineUse exact numbers.\newliney=□ y=\square

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Q. Complete the equation of the line through (−1,6) (-1,6) and (7,−2) (7,-2) .\newlineUse exact numbers.\newliney=□ y=\square
  1. Calculate Slope: To find the equation of a line, we need to determine the slope mm of the line using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of the two points the line passes through.\newlineLet's calculate the slope using the points (−1,6)(-1,6) and (7,−2)(7,-2).\newlinem=−2−67−(−1)=−88=−1m = \frac{-2 - 6}{7 - (-1)} = \frac{-8}{8} = -1
  2. Use 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)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line.\newlineLet's use the point (−1,6)(-1,6) and the slope −1-1 to write the equation.\newliney−6=−1(x−(−1))y - 6 = -1(x - (-1))
  3. Simplify Equation: Simplify the equation by distributing the slope −1-1 into the parentheses.\newliney−6=−1(x+1)y - 6 = -1(x + 1)\newliney−6=−1x−1y - 6 = -1x - 1
  4. Isolate y: To write the equation in slope-intercept form y=mx+by = mx + b, we need to isolate yy on one side of the equation.\newlineAdd 66 to both sides of the equation to isolate yy.\newliney=−1x−1+6y = -1x - 1 + 6\newliney=−1x+5y = -1x + 5
  5. Final Equation: The equation of the line in slope-intercept form is now y=−1x+5y = -1x + 5, which can also be written as y=−x+5y = -x + 5. This is the final answer in standard form with a leading coefficient of 11 for xx.

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