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Question 1008979: I need to find the line parallel to y=4/7x -2/7, which contains the given point (3,-5). I get stuck after solving for y and writing in slope-intercept form. The answer I get is y=4/7x - 12/7 - 20/7, which gives me y=4/7x - 32/7 and I know that's wrong.
Found 2 solutions by macston, Theo:
Answer by macston(5194)   (Show Source):
You can put this solution on YOUR website! y=(4/7)x -(2/7) (red line on graph below)
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If the above equation is correct:
Slope intercept form:
y=mx+b
Where m = the slope = 4/7, y-intercept at (-2/7)
Parallel lines have the same slope,
so the solution will have the form:
y=(4/7)x+b
We know (3,-5) is a solution for the equation,
so we use this point to solve for b:
-5=(4/7)3+b
-5=(12/7)+b
(-35/7)-(12/7)=b
-47/7=b
Put this b in the equation:
y=(4/7)x+b
y=(4/7)x-(47/7) (green line on graph below)
slope=(4/7), y-intercept at (-47/7)
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ANSWER: The equation of the parallel line through (3,-5) is:
y=(4/7)x-(47/7)
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Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! do it this way:
start with the general form of the slope intercept form of the equation for a straight line.
that is y = mx + b
m is the slope and b is the y-intercept.
since the slope has to be the same as the original equation, then m = 4/7 and the equation becomes:
y = 4/7 * x + b
the point that you want to go through is (x,y) = (3,-5).
that means the x-coordinate is 3 and the y-coordinate is -5.
replace y with -5 and replace x with 3 and solve for b.
y = 4/7 * x + b becomes:
-5 = 4/7 * 3 + b
simplify this to get:
-5 = 12/7 + b
subtract 12/7 from both sides of this equation to get:
-5 - 12/7 = b
make common denominators to get:
-35/7 - 12/7 = b
combine like terms to get:
-47/7 = b
your equation of y = 4/7 * x + b now becomes:
y = 4/7 * x - 47/7
that's your parallel line that goes through the point (3,-5).
here's a graph of that equation plus the original equation of y = 4/7 * x - 2/7.
red is the original equation.
blue is the parallel equation that goes through the point (3,-5) as shown.
your alternative was to use the point slope form of the equation for a straight line.
the point slope form is y - y1 = m * (x - x1)
x1,y1 are the coordinates of the point that the line goes through.
your slope is 4/7 as before.
the equation becomes y - y1 = 4/7 * (x - x1)
your point that the line goes through is (3,-5)
replace y1 with -5 and replace x1 with 3 and you get:
y - (-5) = 4/7 * (x - 3)
simplify to get:
y + 5 = 4/7 * (x - 3)
simplify further to get:
y + 5 = 4/7 * x - 3 * 4/7
simplify further to get:
y + 5 = 4/7 * x - 12/7
subtract 5 from both sides of the equation to get:
y = 4/7 * x - 12/7 - 5
make common denominators to get:
y = 4/7 * x - 12/7 - 35/7
combine like terms to get:
y = 4/7 * x - 47/7
same equation as before only you used the point slope form of the equation to get it while before we used the slope intercept form to get it.
both ways are valid.
choose the one you feel more comfortable with.
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