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A line has a slope of −3-3 and includes the points (1,−10)(1,-10) and (0,z)(0,z). What is the value of zz?\newlinez=___z = \_\_\_

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Full solution

Q. A line has a slope of −3-3 and includes the points (1,−10)(1,-10) and (0,z)(0,z). What is the value of zz?\newlinez=___z = \_\_\_
  1. Identify formula for slope: Step 11: Identify the formula for the slope of a line using two points, (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2). The formula is y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}.
  2. Plug in given points: Step 22: Plug in the given points (1,−10)(1, -10) and (0,z)(0, z) into the slope formula. Slope =z−(−10)0−1=z+10= \frac{z - (-10)}{0 - 1} = z + 10.
  3. Set up equation: Step 33: Since the slope of the line is given as −3-3, set up the equation −3=z+10-3 = z + 10.
  4. Solve for z: Step 44: Solve for z. −3=z+10-3 = z + 10. Subtract 1010 from both sides to isolate zz. z=−3−10=−13z = -3 - 10 = -13.

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