SOLUTION: find equation of line that passes through (-3,-3) and is parallel to x-2y=-7

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Question 118614: find equation of line that passes through (-3,-3) and is parallel to x-2y=-7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First convert the standard equation x-2y=-7 into slope intercept form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


1x-2y=-7 Start with the given equation


1x-2y-1x=-7-1x Subtract 1x from both sides


-2y=-1x-7 Simplify


%28-2y%29%2F%28-2%29=%28-1x-7%29%2F%28-2%29 Divide both sides by -2 to isolate y


y+=+%28-1x%29%2F%28-2%29%2B%28-7%29%2F%28-2%29 Break up the fraction on the right hand side


y+=+%281%2F2%29x%2B7%2F2 Reduce and simplify


The original equation 1x-2y=-7 (standard form) is equivalent to y+=+%281%2F2%29x%2B7%2F2 (slope-intercept form)


The equation y+=+%281%2F2%29x%2B7%2F2 is in the form y=mx%2Bb where m=1%2F2 is the slope and b=7%2F2 is the y intercept.








Now let's find the equation of the line that is parallel to y=%281%2F2%29x%2B7%2F2 which goes through (-3,-3)

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is 1%2F2 (its from the slope of y=%281%2F2%29%2Ax%2B7%2F2 which is also 1%2F2). Also since the unknown line goes through (-3,-3), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y%2B3=%281%2F2%29%2A%28x%2B3%29 Plug in m=1%2F2, x%5B1%5D=-3, and y%5B1%5D=-3



y%2B3=%281%2F2%29%2Ax-%281%2F2%29%28-3%29 Distribute 1%2F2



y%2B3=%281%2F2%29%2Ax%2B3%2F2 Multiply



y=%281%2F2%29%2Ax%2B3%2F2-3Subtract -3 from both sides to isolate y

y=%281%2F2%29%2Ax%2B3%2F2-6%2F2 Make into equivalent fractions with equal denominators



y=%281%2F2%29%2Ax-3%2F2 Combine the fractions



y=%281%2F2%29%2Ax-3%2F2 Reduce any fractions

So the equation of the line that is parallel to y=%281%2F2%29%2Ax%2B7%2F2 and goes through (-3,-3) is y=%281%2F2%29%2Ax-3%2F2


So here are the graphs of the equations y=%281%2F2%29%2Ax%2B7%2F2 and y=%281%2F2%29%2Ax-3%2F2



graph of the given equation y=%281%2F2%29%2Ax%2B7%2F2 (red) and graph of the line y=%281%2F2%29%2Ax-3%2F2(green) that is parallel to the given graph and goes through (-3,-3)