Question on point slope formula problem

Dec 2015
50
1
san fransisco
point-slope-question.PNG
it was my understanding that the point slope formula was:

y-y1 = m(x-x1)

Why then, in the solution book have they chosen to use y2 and x2 values in place of y1 and x1? Does it matter which points you choose, or is it meerley two different mathematical models.
Thank you for help.
 

Plato

MHF Helper
Aug 2006
22,490
8,653
View attachment 35107
it was my understanding that the point slope formula was:

y-y1 = m(x-x1)

Why then, in the solution book have they chosen to use y2 and x2 values in place of y1 and x1? Does it matter which points you choose, or is it meerley two different mathematical models.
Thank you for help.
Makes no difference.
 
Apr 2014
46
0
Houston
Right. The "x1" and "y1" shown in the point-slope formula don't necessarily refer to the same coordinates as the "x1" and "y1" in the slope formula. In the point-slope formula, the reason those subscripts of 1 are there is simply to distinguish that an actual value gets plugged into that place, whereas the x and y variables without the subscript are just meant to be left as variables when the equation is written out.
 

Plato

MHF Helper
Aug 2006
22,490
8,653
Right. The "x1" and "y1" shown in the point-slope formula don't necessarily refer to the same coordinates as the "x1" and "y1" in the slope formula. In the point-slope formula, the reason those subscripts of 1 are there is simply to distinguish that an actual value gets plugged into that place, whereas the x and y variables without the subscript are just meant to be left as variables when the equation is written out.
It is more straightforward that that: $\dfrac{y_1-y_2}{x_1-x_2}=\dfrac{y_2-y_1}{x_2-x_1}$.