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A line has a slope of 33 and includes the points (9,u)(9,u) and (10,−1)(10,-1). What is the value of uu?\newlineu=___u = \_\_\_

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Full solution

Q. A line has a slope of 33 and includes the points (9,u)(9,u) and (10,−1)(10,-1). What is the value of uu?\newlineu=___u = \_\_\_
  1. Identify slope formula: Step 11: Identify the formula for the slope between two points.\newlineThe slope formula is (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1). Here, (x1,y1)=(9,u)(x_1, y_1) = (9, u) and (x2,y2)=(10,−1)(x_2, y_2) = (10, -1).
  2. Substitute known values: Step 22: Substitute the known values into the slope formula.\newlineSlope=−1−u10−9\text{Slope} = \frac{{-1 - u}}{{10 - 9}}\newlineSlope=−1−u\text{Slope} = -1 - u
  3. Set equal to given slope: Step 33: Set the calculated slope equal to the given slope of the line, which is 33. \newline3=−1−u3 = -1 - u
  4. Solve for u: Step 44: Solve for u.\newline3+1=−u3 + 1 = -u\newline4=−u4 = -u\newlineu=−4u = -4

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