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

Sep 19, 2016

$\frac{2}{13}$

#### 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 $\text{ } {P}_{1} \to \left({x}_{1} , {y}_{1}\right) = \left(7 , 9\right)$

Let point 2 be $\text{ } {P}_{2} \to \left({x}_{2} , {y}_{2}\right) = \left(- 6 , 7\right)$

$\textcolor{g r e e n}{\text{But "x_2" is less than "x_1 }}$
$\textcolor{g r e e n}{\text{and we should read left to right ( using "x")}}$

${x}_{1} \leftarrow - - - - - - - - - {x}_{2}$
$\textcolor{red}{\uparrow} \text{ direction of reading is wrong} \textcolor{red}{\uparrow}$
$\textcolor{red}{\text{Highest value lowest value }}$

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

Change the order given in the question:

Rewrite as:

Let point 1 be $\text{ } {P}_{1} \to \left({x}_{1} , {y}_{1}\right) = \left(- 6 , 7\right)$

Let point 2 be $\text{ } {P}_{2} \to \left({x}_{2} , {y}_{2}\right) = \left(7 , 9\right)$

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

Slope $= \frac{2}{13}$

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

Note that negative slope is downwards. 