Question 769619
The equation of line in slope-intercept form is {{{y=mx+b}}}
with a number {{{m}}} that is the slope,
and a number {{{b}}} that indicates the y-intercept, meaning that the line passes through (0,b).
 
11. The slope of the line that passes through (-6,8) and (10,-56) is
{{{(-56-8)/(10-(-6))=-64/(10+6)=-64/16=-4}}}
There are many lines with a slope of {{{-4}}}, but a line that passes through those two points must have a slope of {{{-4}}}, so we can eliminate of the choices that have a different slope.  
A {{{y = -4 - 16x }}} is in slope-intercept form and has a slope of {{{-16}}}
B {{{y = - 16  }}} is in slope-intercept form and has a slope of {{{0}}}
{{{highlight(C)}}} {{{4x + y = -16}}} can be transformed into the slope intercept form
{{{4x + y = -16}}}-->{{{y = -16 -4x}}} and has a slope of {{{highlight(-4)}}}
D {{{2x + y = 16}}} can be transformed into the slope intercept form
{{{2x + y = 16}}}-->{{{y = -16 -2x}}} and has a slope of {{{-2}}}
E {{{y = -6 - 8x}}} is in slope-intercept form and has a slope of {{{-8}}}
F {{{y = -16 + 4x}}} is in slope-intercept form and has a slope of {{{4}}} 
 
12.  The slope of the line that passes through (4,5) and (19,-7) is
{{{(-7-5)/(19-4)=-12/15=-3/5=-0.6}}}
There are many lines with a slope of {{{-3/5=-0.6}}}, but a line that passes through those two points must have a slope of {{{-3/5=-0.6}}}, so we can eliminate of the choices that have a different slope.  
A {{{-12x = -123 + 14y}}} can be transformed into the slope intercept form
{{{12x = -123 + 14y}}}-->{{{14y = 12x +123}}}-->{{{y = (12/14)x +123/14}}} and has a slope of {{{12/14=6/7}}}
{{{highlight(B)}}} {{{-12x = -123 + 15y}}}-->{{{-12x +123 =15y}}}-->{{{(-12/15)x +123/15 =y}}} and has a slope of {{{-12/15=highlight(-3/5)}}}  
C {{{-6x = 19 + 5y }}}-->{{{-6x-19=5y }}}-->{{{(-6/5)x-19/5=y }}} has a slope of {{{-6/5}}}
D {{{4x + 5y = 41}}}-->{{{5y = 41-4x}}}-->{{{y=(-4/5)x+41/5}}} has a slope of {{{-4/5}}}
E {{{5x + 5y = 10}}}-->{{{5y =10-5x}}}-->{{{y=(-5/5)x+10/5 }}}-->{{{y=-x+2}}} has a slope of {{{-1}}}
F {{{-16x = 312 - 19y}}}-->{{{-16x-312=-19y}}}-->{{{y=(-16/(-19))x-312/(-19)}}}-->{{{y=(16/19)x-312/19}}} has a slope of {{{16/19}}}