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Find the slope of the line that passes through (2,5)(2, 5) and (9,7)(9, 7). \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 (2,5)(2, 5) and (9,7)(9, 7). \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: (x1,y1)=(2,5)(x_1, y_1) = (2, 5)\newlinePoint 22: (x2,y2)=(9,7)(x_2, y_2) = (9, 7)\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: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. We will plug in the coordinates of the two points into this formula.
  3. Substitute Coordinates: Substitute the coordinates into the slope formula. m=7−59−2m = \frac{7 - 5}{9 - 2}
  4. Perform Subtraction: Perform the subtraction in the numerator and the denominator. m=27m = \frac{2}{7}
  5. Check Simplification: Check for any simplification. Since 22 and 77 are both prime numbers, the fraction 27\frac{2}{7} is already in its simplest form.
  6. Write Final Answer: Write the final answer.\newlineThe slope of the line that passes through the points (2,5)(2, 5) and (9,7)(9, 7) is 27.\frac{2}{7}.

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