Respuesta :
[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 2}}\quad ,&{{ -5}})\quad
% (c,d)
&({{ -4}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-5)}{-4-2}
\\\\\\
m\implies \cfrac{1+5}{-6}\implies \cfrac{6}{-6}\implies -1[/tex]
now, a line parallel to one that has those two points, will also have the same slope, this line has a slope of -1
let's take a peek at [tex]\bf \begin{array}{llll} y=&-x&-5\\ y=&-1x&-5\\ &\quad \uparrow &\quad \uparrow \\ &slope&y-intercept \end{array}[/tex]
notice the slope of that one... recall your y = mx+b, slope-intercept form
now, a line parallel to one that has those two points, will also have the same slope, this line has a slope of -1
let's take a peek at [tex]\bf \begin{array}{llll} y=&-x&-5\\ y=&-1x&-5\\ &\quad \uparrow &\quad \uparrow \\ &slope&y-intercept \end{array}[/tex]
notice the slope of that one... recall your y = mx+b, slope-intercept form
