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In the xy-plane, line m passes through the points (-5,-29) and (10,-2). What is the slope of line m ?

In the xy x y -plane, line m m passes through the points (−5,−29) (-5,-29) and (10,−2) (10,-2) . What is the slope of line m m ?

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Full solution

Q. In the xy x y -plane, line m m passes through the points (−5,−29) (-5,-29) and (10,−2) (10,-2) . What is the slope of line m m ?
  1. Identify given points: Identify the given points on line mm. The points given are (−5,−29)(-5, -29) and (10,−2)(10, -2). We will use these points to calculate the slope of the line.
  2. Use slope formula: Use the slope formula to find the slope of line mm. The slope formula is y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of the two points on the line.
  3. Substitute coordinates: Substitute the coordinates of the given points into the slope formula. Slope m=(−2)−(−29)(10)−(−5)m = \frac{(-2) - (-29)}{(10) - (-5)}
  4. Simplify numerator and denominator: Simplify the numerator and the denominator.\newlineSlope m=−2+2910+5m = \frac{{-2 + 29}}{{10 + 5}}\newlineSlope m=2715m = \frac{{27}}{{15}}
  5. Reduce fraction: Reduce the fraction to its simplest form.\newlineSlope m=2715m = \frac{27}{15} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 33.\newlineSlope m=(27÷315÷3)m = \left(\frac{27 \div 3}{15 \div 3}\right)\newlineSlope m=95m = \frac{9}{5}

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