Question 949421
note: 
A‭ ‬linear function is a function whose graph produces a line.‭  ‬
Linear functions can {{{always}}} be written in the form 
{{{y=mx+b}}} called slope-intercept form

where {{{b‭ }}}‬is the initial or starting value of the function‭ (‬when input,‭{{{x= ‬0}}}‭) or y-intercept‬,‭ ‬
and {{{m }}}is the constant rate of change of the function or a slope.‭ 


1. What is the value of {{{x}}} in the equation {{{3(2x+1)=-15(5x+6)}}}?

{{{3(2x+1)=-15(5x+6)}}}...first reduce, divide both sides by {{{3}}}

{{{(2x+1)=-5(5x+6)}}}....now multiply

{{{2x+1=-25x-30}}}......add {{{25x}}} to the both sides

{{{2x+25x+1=-25x+25x-30}}}

{{{27x+1=-30}}}

{{{27x+1-1=-30-1}}}

{{{27x =-31}}}

{{{highlight(x =-31/27)}}}


2. What is the slope and y-intercept of the equation {{{-2x+3y=-3}}}?

{{{-2x+3y=-3}}}...first write it in slope-intercept form {{{y=mx+b}}} 

{{{3y=2x-3}}}

{{{y=2x/3-3/3}}}

{{{y=(2/3)x-1}}} 

so,  {{{b=-1‭ }}}=> if {{{x=0}}} then {{{y=-1}}} and y-intercept is at the point ({{{0}}},{{{-1}}})

{{{ graph( 600, 600, -10, 10, -10, 10, (2/3)x-1) }}}


3. What is the constant rate of change for the {{{two}}} quantities of {{{10}}} pages read in {{{15}}} minutes?

the {{{two}}} quantities of {{{10}}} pages is {{{20}}} pages

if read in {{{15}}} minutes, then the constant rate of change is 
{{{20pg/15min=4pg/3min=(4/3)(pg/min)=1.333(pg/min)}}} or {{{1}}}{{{1/3}}}{{{(pg/min)}}}