SOLUTION: find an equation of the line containing the point (-1,3) and parallel to the line x+2y=-6

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Question 67126This question is from textbook
: find an equation of the line containing the point (-1,3) and parallel to the line x+2y=-6 This question is from textbook

Found 2 solutions by venugopalramana, Earlsdon:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
find an equation of the line containing the point (-1,3) and parallel to the line x+2y=-6
EQN OF PARALLEL LINE IS
X+2Y=K.......IT PASSES THROUGH (-1,3)...HENCE
-1+2*3=K=5
HENCE EQN . OF REQD. LINE IS
X+2Y=5

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the equation of the line containing the point (-1, 3) and which is parallel to the line whose equation is: x + 2y = -6.
Starting with the knowledge that parallel lines have equal slopes, you can find the slope of the new line by finding the slope of the given line to which it is parallel.
Put the given equation in the slope-intercept form: y = mx + b
x+%2B+2y+=+-6 Subtract x from both sides.
2y+=+-x-6 Now divide both sides by 2.
y+=+%28-1%2F2%29x+-+3 Compare this with:
y+=+mx+%2B+b The slope,m+=+-%281%2F2%29, so now, for the new line, you can write:
y+=+%28-1%2F2%29x+%2B+b
Next, you need to find the value of b, the y-intercept. You can do this by substituting the x- and y-coordinates of the given point (-1, 3) into the above equation and solving for b.
3+=+%28-1%2F2%29%28-1%29+%2B+b Simplify and solve for b.
3+=+1%2F2+%2B+b Subtract 1/2 from both sides.
5%2F2+=+b Now you can write the final equation.
y+=+-%281%2F2%29x+%2B+5%2F2