Question 995091
here you need to use slope-intercept form of equation of the line: {{{y=mx+b}}} where {{{m}}} is the slope and {{{b}}} is y-intercept

use given point ({{{2}}},{{{5}}}) and slope {{{m=3}}} to find y-intercept {{{b}}} 
 
so,we have

{{{5=3*2+b}}}
{{{5=6+b}}}
{{{5-6=b}}}
{{{b=-1}}}

so, your equation is: {{{y=3x-1}}}

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

 
for
({{{-3}}},{{{-1}}}) and slope {{{m=1/2}}}

we have
{{{-1=(1/2)*(-3)+b}}}
{{{-1=-3/2+b}}}
{{{-1+3/2=b}}}
{{{-2/2+3/2=b}}}

{{{b=1/2}}}

 equation is: {{{y=(1/2)x+1/2}}}


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


for

({{{-3}}},{{{4}}}), ({{{1}}},{{{12}}})

we have

{{{4=m*(-3)+b}}}

{{{4=-3m+b}}}.........eq.1

{{{12=m*(1)+b}}}

{{{12=m+b}}}.........eq.2

subtract eq.1 from eq.2

{{{12-4=m+b-(-3m+b)}}}

{{{8=m+cross(b)+3m-cross(b)}}}

{{{8=4m}}}

{{{m=2}}}

go to {{{4=-3m+b}}}.........eq.1 substitute {{{2}}} for {{{m}}} and solve for {{{b}}}

{{{4=-3*2+b}}}
{{{4=-6+b}}}

{{{4+6=b}}}

{{{b=10}}}

equation is: {{{y=2x+10}}}


{{{drawing( 600, 600, -10, 10, -10, 15,
circle(-3,4,.12), locate(-3,4,p(-3,4)),
circle(1,12,.12), locate(1,12,p(1,12)),
 graph( 600, 600, -10, 10, -10, 15, 2x+10)) }}}


for

({{{-1}}},{{{6}}}) ({{{2}}},{{{4}}})

{{{6=m*(-1)+b}}}

{{{6=-m+b}}}.........eq.1

{{{4=m*(2)+b}}}

{{{4=2m+b}}}.........eq.2
-------------------

{{{6-4=-m+b-(2m+b)}}}

{{{2=-m+b-2m-b}}}

{{{2=-3m}}}

{{{m=-2/3}}}

{{{4=2(-2/3)+b}}}.........eq.2

{{{4=(-4/3)+b}}}

{{{4+4/3=b}}}

{{{12/3+4/3=b}}}

{{{16/3=b}}}

equation is: {{{y=-(2/3)x+16/3}}}


{{{drawing( 600, 600, -10, 10, -10, 15,
circle(2,4,.12), locate(2,4,p(2,4)),
circle(-1,6,.12), locate(-1,6,p(-1,6)),
 graph( 600, 600, -10, 10, -10, 15, -(2/3)x+16/3)) }}}


for

({{{2}}},{{{1}}}) and slope {{{m=0}}}

{{{1=0*(2)+b}}}

{{{b=1}}}


equation is: {{{y=1}}} (horizontal line)


{{{drawing( 600, 600, -10, 10, -10, 15,
circle(2,1,.12), locate(2,1,p(2,1)),
 graph( 600, 600, -10, 10, -10, 15, 1)) }}}