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A line that includes the points (2,−1)(2,-1) and (3,z)(3,z) has a slope of 77. What is the value of zz?\newlinez=___z = \_\_\_

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Full solution

Q. A line that includes the points (2,−1)(2,-1) and (3,z)(3,z) has a slope of 77. What is the value of zz?\newlinez=___z = \_\_\_
  1. Identify Points and Slope: Identify the points and the slope.\newlinePoints: (2,−1)(2, -1) and (3,z)(3, z)\newlineSlope =7= 7\newlineUse the slope formula: Slope =y2−y1x2−x1= \frac{y_2 - y_1}{x_2 - x_1}\newline7=z−(−1)3−27 = \frac{z - (-1)}{3 - 2}
  2. Use Slope Formula: Simplify and solve for zz.7=z+117 = \frac{z + 1}{1}Multiply both sides by 11 to isolate z+1z + 1.7×1=(z+1)7 \times 1 = (z + 1)7=z+17 = z + 1
  3. Simplify and Solve: Subtract 11 from both sides to find zz.\newline7−1=z7 - 1 = z\newlinez=6z = 6

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