Algebra · real student question

Find the slope of the line that passes through the points (2, 5) and (3, -3).

Question

Use

m=y2−y1x2−x1m=\frac{y_2-y_1}{x_2-x_1}

to find the slope of the line through (2,5)(2,5) and (3,−3)(3,-3).

Step-by-step solution

  1. Label the coordinates before touching the formula. Most sign errors in this problem come from mixing up which point is which, so commit to one assignment and keep it:

    (x1,y1)=(2,5),(x2,y2)=(3,−3).(x_1,y_1)=(2,5),\qquad (x_2,y_2)=(3,-3).

  2. Compute the rise (the change in y). Subtract in the same order as the labels, and keep the brackets around the negative coordinate:

    y2−y1=(−3)−5=−8.y_2-y_1=(-3)-5=-8.

  3. Compute the run (the change in x).

    x2−x1=3−2=1.x_2-x_1=3-2=1.

  4. Divide rise by run.

    m=−81=−8.m=\frac{-8}{1}=-8.

  5. Sanity-check the sign and the order. A negative slope means the line falls as xx increases, which matches going from y=5y=5 down to y=−3y=-3. Reversing both subtractions also works, since

    5−(−3)2−3=8−1=−8;\frac{5-(-3)}{2-3}=\frac{8}{-1}=-8;

    what you must never do is reverse only one of them.

Answer

m=−8m=-8

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