Help with some algebra

Question

Can anybody explain to me how they went from this

$$y − y_1 = \frac{y_2 − y_1}{x_2 − x_1} (x − x_1)$$

to this.

$$(y_1 − y_2 )·x − (x_1 − x_2)·y − (y_1 − y_2 )·x_1 + (x_1 − x_2)·y_1 = 0$$

Its confusing..

Answer 1

Ok! So you just got to multiply by $(x_2-x_1)$ on both sides to obtain

$$(y-y_1)(x_2-x_1)=(y_2-y_1)(x-x_1)$$

Now you can expand by multiplying each bracket to obtain:

$$y(x_2-x_1)-y_1(x_2-x_1)=x(y_2-y_1)-x_1(y_2-y_1)$$

Where in the right hand side, I multiplied each term of the second bracket by the whole first bracket. Now observe that $(x_2-x_1)=-(x_1-x_2)$ and the same with $(y_2-y_1)=-(y_1-y_2)$, you can see this since

$$-(x_1-x_2)=-x_1+x_2=x_2-x_1$$

Can you finish it?