Question

What is the slope of the line passing through the following points: # (-6, 7), (-7,-2)) #?

Answer 1

Slope `= 9`

Explanation:

The slope is defined as `("change in " y)/("corresponding change in "x)`

In the general case, given two points `(x_1,y_1)` and `(x_2,y_2)`, the slope can be determined as:
`color(white)("XXX")m=(y_1-y_2)/(x_1-x_2)`

For the given example we have
`color(white)("XXX")(x_1,y_1) = (-6,7)`
`color(white)("XXX")(x_2,y_2)=(-7,-2)`
and therefore
`color(white)("XXX")m=(7-(-2))/(-6-(-7)) = 9/1 = 9`