Question

Which line is parallel to the line that passes through the points (2, –5) and (–4, 1)? a. y=-x-5

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 2}}\quad ,&{{ -5}})\quad % (c,d) &({{ -4}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-5)}{-4-2} \\\\\\ m\implies \cfrac{1+5}{-6}\implies \cfrac{6}{-6}\implies -1$

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 $\bf \begin{array}{llll} y=&-x&-5\\ y=&-1x&-5\\ &\quad \uparrow &\quad \uparrow \\ &slope&y-intercept \end{array}$

notice the slope of that one... recall your y = mx+b, slope-intercept form

Answer 2

The answer is D
the answer is D