Question 944988
the equation of a line in slope-intercept form:

{{{y=mx+b}}} where {{{m}}} is a slope and {{{b}}} y-intercept

we will use given points ({{{6}}},{{{ 1}}}) and ({{{-10}}}, {{{9}}}) to set up system and solve it for {{{m}}} and {{{b}}}


{{{y=mx+b}}} if ({{{6}}},{{{ 1}}}) then we have

{{{1=m*6+b}}}

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

{{{y=mx+b}}} if ({{{-10}}},{{{ 9}}}) then we have

{{{9=m*(-10)+b}}}

{{{9=-10m+b}}}.....eq.2

so, the system is:

{{{1=6m+b}}}.....eq.1
{{{9=-10m+b}}}.....eq.2
----------------------------------

start with {{{1=6m+b}}}.....eq.1, solve for {{{b}}}

{{{1-6m=b}}}...substitute in eq.2


{{{9=-10m+1-6m}}}.....eq.2, solve for {{{m}}}

{{{9-1=-16m}}}

{{{8=-16m}}}

{{{16m=-8}}}

{{{m=-8/16}}}

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


now find {{{b}}}

{{{b=1-6m}}}

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

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

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

{{{b=1+3}}}

{{{b=4}}} 

so, your equation is: {{{y=-(1/2)x+4}}}

and your answer is  a.) 


{{{drawing( 600, 600, -15,15, -15, 15,
locate(-10,9,p(-10,9)),locate(6,1,p(6,1)),
circle(-10,9,.2),circle(6,1,.2), graph( 600, 600, -15,15, -15, 15, -(1/2)x+4)) }}}