Question 1091764

{{{y=mx+b}}}


the line containing the given point ({{{4}}},{{{5}}})
and parallel to the line {{{x+6y=7}}}

recall, parallel lines have same slope {{{m}}}; so, first find a slope of given line

{{{x+6y=7}}}
{{{6y=-x+7}}}
{{{y=highlight(-(1/6))x+7/6}}}=>slope {{{m=-(1/6)}}}

so far, your line is {{{y=-(1/6)x+b}}}

{{{y=-(1/6)x+b}}}.... plug in coordinates of given point ({{{4}}},{{{5}}}), and find {{{b}}}

{{{5=-(1/6)(4)+b}}}

{{{5=-(4/6)+b}}}

{{{5+(4/6)=b}}}

{{{30/6+4/6=b}}}

{{{b=34/6}}}

{{{b=17/3}}}

your line is {{{y=-(1/6)x+17/3}}}


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(4,5,.12),locate(4,5,p(4,5)),
 graph( 600, 600, -10, 10, -10, 10,-(1/6)x+17/3)) }}}