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Find the slope of the line that passes through (10,4)(10, 4) and (1,8)(1, 8).\newlineSimplify your answer and write it as a proper fraction, improper fraction, or integer.\newline_____

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Full solution

Q. Find the slope of the line that passes through (10,4)(10, 4) and (1,8)(1, 8).\newlineSimplify your answer and write it as a proper fraction, improper fraction, or integer.\newline_____
  1. Identify Coordinates: Identify the coordinates of the two points.\newlinePoint 11: (10,4)(10, 4)\newlinePoint 22: (1,8)(1, 8)\newlineWe will use these coordinates to calculate the slope of the line.
  2. Recall Slope Formula: Recall the formula for the slope mm of a line given two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is:\newlinem=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
  3. Substitute Coordinates: Substitute the coordinates of the two points into the slope formula.\newlineUsing Point 11 (10,4)(10, 4) as (x1,y1)(x_1, y_1) and Point 22 (1,8)(1, 8) as (x2,y2)(x_2, y_2), we get:\newlinem=8−41−10m = \frac{8 - 4}{1 - 10}
  4. Calculate Differences: Calculate the difference in the y-coordinates and the x-coordinates.\newlineDifference in y-coordinates: 8−4=48 - 4 = 4\newlineDifference in x-coordinates: 1−10=−91 - 10 = -9
  5. Calculate Slope: Calculate the slope using the differences.\newlinem=4−9m = \frac{4}{-9}\newlineThe slope of the line is −49-\frac{4}{9}.

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