Question

What is the slope of the line passing through the following points: `(-5, 4) ,(7, -2)`?

Answer 1

Slope= `-1/2`

Explanation:

Slope is defined as `(Delta y)/ (Delta x)` . In other words, it is the change in `y` over the change in `x`. When we have two points, we can calculate the slope by subtracting the corresponding values and making them into a ratio.

`x-y` coordinate points are in the form `(x,y)`
We have `(-5,4)` and `(7,-2)`
Let's call `(-5,4)=(x_1,y_1)` and `(7,-2)=(x_2,y_2)`
Now, it doesn't matter which point you choose to subtract from which point- it will work either way, as you can see below when calculating the slope:

`(Delta y)/ (Delta x)=(y_2-y_1)/(x_2-x_1)=(-2-4)/(7--5)=(-2-4)/(7+5)=(-6)/12=-1/2`

Is equivalent to the other way around:

`(Delta y)/ (Delta x)=(y_1-y_2)/(x_1-x_2)=(4--2)/(-5-7)=(4+2)/(-5-7)6/-12=-1/2`

Just make sure you are consistent in the order you subtract.