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The points (−5,−4)(-5,-4) and (−4,z)(-4,z) fall on a line with a slope of −6-6. What is the value of zz?\newlinez=___z = \_\_\_

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Q. The points (−5,−4)(-5,-4) and (−4,z)(-4,z) fall on a line with a slope of −6-6. What is the value of zz?\newlinez=___z = \_\_\_
  1. Identify Given Points and Slope: Identify the given points and the slope.\newlineWe have the points (−5,−4)(-5, -4) and (−4,z)(-4, z) and the slope of the line is −6-6.
  2. Use Slope Formula: Use the slope formula to set up an equation.\newlineThe slope formula is (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1). Let's plug in our values.\newline−6=(z−(−4))/(−4−(−5))-6 = (z - (-4)) / (-4 - (-5))
  3. Simplify Equation: Simplify the equation.\newline−6=z+4−4+5-6 = \frac{z + 4}{-4 + 5}\newline−6=z+41-6 = \frac{z + 4}{1}
  4. Solve for z: Solve for z.\newlineMultiply both sides by 11 to isolate zz.\newline−6×1=(z+4)-6 \times 1 = (z + 4)\newline−6=z+4-6 = z + 4
  5. Subtract to Find z Value: Subtract 44 from both sides to find the value of zz. \newline−6−4=z+4−4-6 - 4 = z + 4 - 4\newline−10=z-10 = z

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