Question 1011791
 part a: An equation that makes a straight line when it is graphed.

Often written in the form: {{{y = mx+b}}}

 what it means:

{{{y }}}= how far up

{{{x}}} = how far along

{{{m}}} = Slope or Gradient (how steep the line is)

{{{b}}} = the y-intercept (where the line crosses the y axis)

How do you find "{{{m}}}" and "{{{b}}}"? 


    {{{b}}} is easy: just see where the line crosses the {{{y}}} axis and you do it by setting {{{x=0 }}} in given equation and solving for {{{y}}}

   {{{ m}}} (the Slope) needs some calculation:

 {{{ m=(change_in_y)/(change_in_x)}}} which means if you are given two points that lie on a line and their coordinates are ({{{x[1]}}},{{{y[1]}}}) and ({{{x[2]}}},{{{y[2]}}}), then slope is

{{{ m=(y[1]-y[2])/(x[1]-x[2])}}}


Example: {{{y = 2x + 1}}}

{{{y = 2*0 + 1}}}=>{{{y =  1}}} =>{{{b=1}}} => y-intercept is at ({{{0}}},{{{1}}})

 {{{y = highlight(2)x + 1}}}=>{{{m=2}}}

to graph it make a table for two points

{{{x}}}|{{{y}}}

{{{0}}}|{{{1}}}...we already have it

{{{-1}}}|{{{-1}}}.....choose any value for {{{x}}} and find the matching value for {{{y}}}; if {{{x=-1}}} then {{{y = 2(-1) + 1}}}=>{{{y=-1}}}

plot points and draw a line through

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(0,1,.12),circle(-1,-1,.12),
locate(0,1,p(0,1)),locate(-1,-1,p(-1,-1)),
 graph( 600, 600, -10, 10, -10, 10, 2x + 1)) }}}



Example: you might be given a graph like this

{{{graph( 600, 600, -10, 10, -10, 10, -3x )) }}}

 and asked to find the equation of that line {{{y=mx+b}}}

first what we see from the graph is that the line goes through origin; so, we know that {{{b=0}}}

so, your equation will be {{{y=mx+0}}} or just {{{y=mx}}} and we need to find a slope {{{m}}}

as you see from a graph, if {{{x=-1}}} that {{{y=3}}} and if {{{x=0}}} that {{{y=0}}}

so, you have points

({{{x[1]}}},{{{y[1]}}})=({{{0}}},{{{0}}}) 
and 
({{{x[2]}}},{{{y[2]}}})=({{{-1}}},{{{3}}})

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(0,0,.12),circle(-1,3,.12),
locate(0,0,p(0,0)),locate(-1,3,p(-1,3)),graph( 600, 600, -10, 10, -10, 10, -3x )) }}}


then you can find the slope:

{{{ m=(y[1]-y[2])/(x[1]-x[2])}}}

{{{ m=(0-3)/(0-(-1))}}}

{{{ m=(0-3)/(0+1)}}}

{{{ m=-3/1}}}

{{{ m=-3}}}

and your equation is {{{highlight(y=-3x)}}}