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A line has a slope of −7-7 and includes the points (−6,c)(-6,c) and (−5,−6)(-5,-6). What is the value of cc?\newlinec=c = ____

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Full solution

Q. A line has a slope of −7-7 and includes the points (−6,c)(-6,c) and (−5,−6)(-5,-6). What is the value of cc?\newlinec=c = ____
  1. Substitute values into formula: We know the formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}. Here, the slope is given as −7-7, and the points are (−6,c)(-6, c) and (−5,−6)(-5, -6).
  2. Simplify the denominator: Substitute the values into the slope formula: −7=−6−c−5+6-7 = \frac{-6 - c}{-5 + 6}.
  3. Isolate the numerator: Simplify the denominator: −7=−6−c1-7 = \frac{-6 - c}{1}.
  4. Solve for cc: Multiply both sides by 11 to isolate the numerator: −7=−6−c-7 = -6 - c.
  5. Final calculation: Solve for cc: c=−6+7c = -6 + 7.
  6. Final calculation: Solve for cc: c=−6+7c = -6 + 7. Final calculation: c=1c = 1.

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