Question

A student finds the slope of the line between (8,17,) and (1,4) she writes 17-4/1-8 What mistake did she make?

Answer 1

The first mistake is that she didn't use parenthesis to indicate we're dividing all of one thing (numerator) over all of another expression (denominator)

slope = rise/run = numerator/denominator

So she should write (17-4)/(1-8) to indicate all of "17-4" is divided over all of "1-8"

However, there's another error that your teacher is probably more focused on. Note how 17-4 represents subtracting the y coordinates from left to right. We start with the left point y coordinate 17 and subtract off the right point y coordinate 4

left y - right y = 17 - 4

But then the student swaps the order when they wrote 1-8. Instead it should be 8-1

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Here's what they should have written (17-4)/(8-1)

This is the same as (4-17)/(1-8)

We can subtract in any order as long as it stays consistent between the numerator and denominator