Question 192344
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1.Find the slope of the line that passes through the points (3, -5) and (-4, -6). 


Via Point-Slope Form:
{{{m=(y[2]-y[1])/(x[2]-x[1])=(-6-(-5))/(-4-3)=(-6+5)/(-7)=-1/-7}}}
{{{red(m=1/7)}}}, Answer


Let's check thru point (3,-5) via Slope-Intercept form, {{{system(y=mx+b)}}}
{{{-5=(1/7)(3)+b}}}
{{{b=-5-3/7=(-35-3)/7}}}
{{{b=-38/7}}}, or {{{b=-5.428}}}, Y-Interecpt


It follows your Line Eqn, {{{red(y=(1/7)x-38/7)}}}


We'll see graph,
{{{drawing(400,400,-10,10,-10,3,grid(1),graph(400,400,-10,10,-10,3,(1/7)x-38/7),blue(circle(3,-5,.15)),blue(circle(-4,-6,.15)))}}}



2.Find the equation in slope-intercept form, of the line that passes through the points (3, 6) and (-7, -3); write equation in slope-intercept form.


First we find the Slope:
{{{m=(y[2]-y[1])/(x[2]-x[1])=(-3-6)/(-7-3)=-9/-10}}}
{{{red(m=9/10)}}}


Then thru point (3,6) via Slope-Intercept Form,{{{system(y=mx+b)}}}
{{{6=(9/10)(3)+b}}}---> {{{6=27/10+b}}}
{{{b=6-27/10=(60-27)/10}}}
{{{red(b=33/10)}}}, or {{{b=3.3}}}


It follows, {{{red(y=(9/10)x+33/10)}}}, Answer


Let us see,
{{{drawing(400,400,-10,10,-8,8,grid(1),graph(400,400,-10,10,-8,8,(9/10)x+33/10),blue(circle(3,6,.15)),blue(circle(-7,-3,.15)))}}}


Thank you,
Jojo</font>