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The points (2,z)(2,z) and (3,−10)(3,-10) fall on a line with a slope of −8-8. What is the value of zz?\newlinez = ____

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Full solution

Q. The points (2,z)(2,z) and (3,−10)(3,-10) fall on a line with a slope of −8-8. What is the value of zz?\newlinez = ____
  1. Identify Given Points and Slope: Identify the given points and slope.\newlineWe have the points (2,z)(2, z) and (3,−10)(3, -10) and a slope of −8-8.\newlineWe will use the slope formula, which is (y2−y1)/(x2−x1)=slope.(y_2 - y_1) / (x_2 - x_1) = \text{slope}.
  2. Plug Values into Formula: Plug the values into the slope formula.\newline−8=−10−z3−2-8 = \frac{-10 - z}{3 - 2}\newlineSimplify the denominator.\newline−8=−10−z1-8 = \frac{-10 - z}{1}
  3. Simplify Denominator: Solve for zz.\newlineMultiply both sides by 11 to get rid of the denominator.\newline−8×1=(−10−z)×1-8 \times 1 = (-10 - z) \times 1\newline−8=−10−z-8 = -10 - z
  4. Solve for zz: Isolate zz.\newlineAdd 1010 to both sides of the equation.\newline−8+10=−10+10−z-8 + 10 = -10 + 10 - z\newline2=−z2 = -z
  5. Isolate zz: Solve for zz by multiplying both sides by −1-1.2×−1=−z×−12 \times -1 = -z \times -1−2=z-2 = z

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