If we say
[tex]y-y_1=m(x-x_1)[/tex]
then dividing both sides by (x - x_1) gives
[tex]\frac{1}{x-x_1}\times(y-y_1)=m(x-x_1)\times\frac{1}{x-x_1}[/tex]
[tex]\therefore m=\frac{y-y_1}{x-x_1}[/tex]
which is our answer!
The above equation correctly gives the slope m because it is in accord with the definition of m as rise / run.
(E).
Let us now expand the RHS of the first equation to get:
[tex]y-y_1=mx-mx_1[/tex]
Adding y_1 to both sides gives
[tex]\textcolor{#FF7968}{y=mx-mx_1+y_{1.}}[/tex]
Or in a more neat form
[tex]\textcolor{#FF7968}{y=mx+(y_1-mx_1)}\text{\textcolor{#FF7968}{.}}[/tex]
(F).
As can be seen from the equation y = mx + b we got in E, the y-intercept b is given by
[tex]\textcolor{#FF7968}{b=y_1-mx_{1.}}[/tex]
