Question

What is the slope of the line passing through `(7,9) ;(-6,7)`?

Answer 1

`2/13`

Explanation:

Slope (gradient) is the change in the y-axis compered to the appropriate change in the x-axis.

Slope`" "-> ("change in y")/("change in x")` reading left to right on the graph.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider the order given in the question

Let point 1 be `" "P_1->(x_1,y_1)=(7,9)`

Let point 2 be `" "P_2->(x_2,y_2)=(-6,7)`

`color(green)("But "x_2" is less than "x_1 ")`
`color(green)("and we should read left to right ( using "x")")`

`x_1 larr---------x_2`
`color(red)(uarr)" direction of reading is wrong" color(red)(uarr)`
`color(red)("Highest value lowest value ")`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Change the order given in the question:

Rewrite as:

Let point 1 be `" "P_1->(x_1,y_1)=(-6,7)`

Let point 2 be `" "P_2->(x_2,y_2)=(7,9)`

Slope`" "-> ("change in y")/("change in x") =(y_2-y_1)/(x_2-x_1) =(9-7)/(7-(-6))`

Slope `=2/13`

Positive slope means that the graph line is going upwards as you read left to right.

Note that negative slope is downwards.