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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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Full solution

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 the slope: To find the equation of a line, we need to determine the slope mm of the line using the formula m=(y2−y1)(x2−x1)m = \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=(−2−6)(7−(−1))m = \frac{(-2 - 6)}{(7 - (-1))}\newlinem=(−8)(8)m = \frac{(-8)}{(8)}\newlinem=−1m = -1
  2. Write the 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))\newliney−6=−1(x+1)y - 6 = -1(x + 1)
  3. Simplify the equation: Next, we simplify the equation by distributing the slope −1-1 across the terms in the parentheses.\newliney−6=−1×x−1×1y - 6 = -1 \times x - 1 \times 1\newliney−6=−x−1y - 6 = -x - 1
  4. Convert to slope-intercept form: To write the equation in slope-intercept form y=mx+by = mx + b, we need to solve for yy.
    y=−x−1+6y = -x - 1 + 6
    y=−x+5y = -x + 5

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