Question 1152279
Write the slope-intercept ({{{y=mx+b}}})form of:

1. Slope equals {{{2}}} and the line goes through the point ({{{-1}}},{{{ 3}}})

{{{m=2}}}, ({{{x=-1}}},{{{y= 3}}})

plug it in {{{y=mx+b}}} and solve for {{{b}}}

{{{3=2(-1)+b}}}

{{{3=-2+b}}}

{{{b=3+2}}}

{{{b=5}}}

your equation is:  {{{y=2x+5}}}

{{{drawing( 600,600, -10, 10, -10, 10, 
circle(-1,3,.12),locate(-1,3,p(-1,3)),

 graph( 600,600, -10, 10, -10, 10, 2x+5)) }}}



2. The line goes through the points ({{{8}}},{{{5}}}) and ({{{9}}}, {{{6}}})

use given points to find a slope:

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

{{{m=(6-5)/(9-8)}}}

{{{m=1}}}

so far

{{{y=1x+b}}}.....use one point to find {{{b}}}

{{{5=1*8+b}}}

{{{b=5-8}}}

{{{b=-3}}}


your equation is:{{{y=x-3}}}

{{{drawing( 600,600, -10, 15, -10, 10, 
circle(9,6,.12),locate(9,6,p(9,6)),
circle(8,5,.12),locate(8,5,p(8,5)),
 graph( 600,600, -10, 15, -10, 10, x-3)) }}}


3. The line goes through the points 
({{{-1}}}, {{{-7}}}) and ({{{-8}}}, {{{-2}}})

use given points to find a slope:

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

{{{m=(-2-(-7))/(-8-(-1))}}}

{{{m=(-2+7)/(-8+1)}}}

{{{m=5/-7}}}

{{{m=-5/7}}}

so far

{{{y=-(5/7)x+b}}}.....use one point to find {{{b}}}

{{{-7=-(5/7)(-1)+b}}}

{{{-7=(5/7)+b}}}

{{{-49/7-5/7=b}}}

{{{b=-54/7}}}


your equation is: {{{y=-(5/7)x-54/7}}}



{{{drawing( 600,600, -10, 10, -10, 10, 
circle(-1,-7,.12),locate(-1,-7,p(-1,-7)),
circle(-8,-2,.12),locate(-8,-2,p(-8,-2)),
 graph( 600,600, -10, 10, -10, 10, -(5/7)x-54/7)) }}}



4. The line goes through the points 

({{{1/2}}}, {{{3/2}}}) and ({{{-1/4}}}, {{{5/4}}})

use given points to find a slope:

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

{{{m=(5/4-3/2)/(-1/4-1/2)}}}

{{{m=(5/4-6/4)/(-1/4-2/4)}}}

{{{m=(-1/cross(4))/(-3/4)}}}

{{{m=1/3}}}

so far

{{{y=(1/3)x+b}}}.....use one point to find {{{b}}}

{{{3/2=(1/3)(1/2)+b}}}

{{{3/2=(1/6)+b}}}

{{{3/2-(1/6)=b}}}

{{{9/6-(1/6)=b}}}

{{{b=8/6}}}

{{{b=4/3}}}

your equation is: {{{y=(1/3)x+4/3}}}

{{{drawing( 600,600, -10, 10, -10, 10, 
circle(1/2,3/2,.12),locate(1/2,2,p(1/2,3/2)),
circle(-1/4,5/4,.12),locate(-1.5,1,p(-1/4,5/4)),
 graph( 600,600, -10, 10, -10, 10, (1/3)x+4/3)) }}}