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Complete the point-slope equation of the line (−9,6)(-9,6) through (−7,−8)(-7,-8) and Use exact numbers.

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Full solution

Q. Complete the point-slope equation of the line (−9,6)(-9,6) through (−7,−8)(-7,-8) and Use exact numbers.
  1. Calculate Slope: Find the slope of the line using the two given points.\newlineThe slope mm is calculated 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.\newlineLet's use (−9,6)(-9, 6) as (x1,y1)(x_1, y_1) and (−7,−8)(-7, -8) as (x2,y2)(x_2, y_2).\newlinem=−8−6−7−(−9)m = \frac{-8 - 6}{-7 - (-9)}\newlinem=−142m = \frac{-14}{2}\newlinem=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}00
  2. Use Point-Slope Form: Use the point-slope form of the equation of a line. The point-slope form 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. We can use either of the two points given, but let's use (−9,6)(-9, 6) for this example. y−6=−7(x−(−9))y - 6 = -7(x - (-9)) y−6=−7(x+9)y - 6 = -7(x + 9)
  3. Simplify Equation: Simplify the equation if necessary.\newlineIn this case, the equation is already in point-slope form, so no further simplification is needed.\newlineThe final point-slope equation of the line is y−6=−7(x+9)y - 6 = -7(x + 9).

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