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A line with a slope of −5-5 passes through the points (0,−1)(0,-1) and (−1,z)(-1,z). What is the value of zz?\newlinez = ____

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Full solution

Q. A line with a slope of −5-5 passes through the points (0,−1)(0,-1) and (−1,z)(-1,z). What is the value of zz?\newlinez = ____
  1. Understand slope concept: Understand the concept of slope. The slope of a line is the ratio of the change in the yy-coordinate to the change in the xx-coordinate between two points on the line. The formula for slope (mm) is given by: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1} Here, we are given the slope (mm) as −5-5 and two points on the line: (0,−1)(0, -1) and (−1,z)(-1, z).
  2. Substitute values into formula: Substitute the given values into the slope formula.\newlineUsing the points (0,−1)(0, -1) as (x1,y1)(x_1, y_1) and (−1,z)(-1, z) as (x2,y2)(x_2, y_2), we can plug these into the slope formula:\newline−5=z−(−1)−1−0-5 = \frac{z - (-1)}{-1 - 0}
  3. Simplify equation and solve: Simplify the equation and solve for zz.−5=z+1−1-5 = \frac{z + 1}{-1}To find zz, we multiply both sides by −1-1:−5×−1=(z+1)-5 \times -1 = (z + 1)5=z+15 = z + 1
  4. Isolate variable zz: Subtract 11 from both sides to isolate zz.\newline5−1=z5 - 1 = z\newline4=z4 = z

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