Question 967582

the equation of the line which passes through the point ( {{{-2}}},{{{ 1}}} ) and is parallel to the straight line with the equation {{{2x - y - 3 = 0}}}:

recall: parallel lines have same slope
{{{2x - y - 3 = 0}}}...write in slope-intercept form to see what is a slope

{{{y=highlight(2)x - 3 }}}=> a slope is {{{highlight(2)}}}, so parallel line will have same slope

equation is {{{y=2x+b}}} so far

now use given point ( {{{-2}}},{{{ 1}}} ) and find {{{b}}}

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

{{{1=-4+b}}}

{{{1+4=b}}}

{{{5=b}}}

then, your equation is {{{y=2x+5}}}

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