Question 1205256
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I have seen countless examples of where a student blindly plugs numbers into the textbook formula for finding the slope of a line through two points and gets the wrong answer by plugging the wrong numbers in the wrong places.<br>
Plugging numbers into a formula doesn't help you learn anything.  I always encourage students to use an informal common sense method for finding a slope.<br>
Somewhat informally, slope is defined as "rise over run".  Even more informally, the slope tells you how much you move up or down as you move 1 unit to the right.<br>
So to find the slope of the line through the two given points, first make sure you are moving from left to right; then determine how far you are moving right (run) and how far you are moving up or down (rise); then find the ratio of rise to run.<br>
The second given point is farther to the left (x=1 is to the left of x=10), so start at (1,9) and move to (10,8).  The run (change in x) is from 1 to 10, a difference of 9; the rise (change in y) is from 9 to 8, a difference of -1; so the slope is rise/run = -1/9.<br>
You will understand math better, and enjoy it more, if you use methods that let you see what you are doing, instead of relying on magic formulas.<br>
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It's beyond my understanding why anyone who considers themselves a "teacher" of mathematics would say it is stupid for a student to understand mathematics, instead advocating for teaching the student to do mathematics by plugging numbers into formulas....<br>