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A line that includes the points (9,−10)(9,-10) and (7,j)(7,j) has a slope of −9-9. What is the value of jj?\newlinej=___j = \_\_\_

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Q. A line that includes the points (9,−10)(9,-10) and (7,j)(7,j) has a slope of −9-9. What is the value of jj?\newlinej=___j = \_\_\_
  1. Understand the slope formula: Understand the formula for the slope of a line. The slope mm of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}.
  2. Apply formula to given points: Apply the slope formula to the given points and slope.\newlineWe know the slope m=−9m = -9, and we have the points (9,−10)(9, -10) and (7,j)(7, j). Let's plug these into the slope formula:\newline−9=j−(−10)7−9-9 = \frac{j - (-10)}{7 - 9}
  3. Simplify the equation: Simplify the equation.\newline−9=(j+10)(7−9)-9 = \frac{(j + 10)}{(7 - 9)}\newline−9=(j+10)(−2)-9 = \frac{(j + 10)}{(-2)}
  4. Solve for j: Solve for j.\newlineTo find jj, we need to multiply both sides of the equation by −2-2:\newline−9×−2=(j+10)-9 \times -2 = (j + 10)\newline18=j+1018 = j + 10
  5. Subtract 1010 to isolate jj: Subtract 1010 from both sides to isolate jj.18−10=j18 - 10 = j8=j8 = j

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