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Question 117997: Find the equation of each line. Write each answer in clope intercept form.
The line is parallel to -3x + 2y = 9 and contains the point (-2,-1).
I got 2y=-3x + 9 which is slope intercept form
answer I got was y= 3/2x + 4 which is incorrect
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given the line having the equation:
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-3x + 2y = 9
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To find a line parallel to this you need to first determine the slope of the given line. One
way to do that is to convert the equation of the given line into slope-intercept form.
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Start with the equation given. Isolate the term containing y on the left side by getting rid
of the -3x term on the left side. You can do that by adding +3x to both sides. This addition
converts the given equation to:
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2y = 3x + 9
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Solve for y by dividing both sides (all terms) by 2 to get:
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y = (3/2)x + 9/2
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This is now in slope intercept form and you can tell from this form that the slope of the
line it defines is (3/2). So any parallel line will have the same slope. Therefore,
a parallel line will have a slope intercept equation of the form:
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y = (3/2)x + b
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Then you are told that the parallel line must go through the point (-2, -1). That means that
the equation must be satisfied if x = -2 and y = -1. Substitute these two values appropriately
into the slope intercept equation for this parallel line and you have:
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-1 = (3/2)(-2) + b
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Do the multiplication on the right side and you have:
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-1 = (3*(-2))/2 + b
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which further simplifies to:
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-1 = -3 + b
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Solve for b by adding +3 to both sides:
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+2 = b
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Now that you know b = +2 you can return to the slope intercept form for the parallel line:
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y = (3/2)x + b
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and substitute +2 for b to get the slope intercept form of the equation that you are looking for as:
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y = (3/2)x + 2
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This is the equation of a line that is parallel to the given line. It intercepts the y-axis
at +2 and its slope is 3/2. It also passes through the point (-2, -1) as required by
the problem.
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You can get your answer into standard form. Begin by multiplying both sides of the slope
intercept form (all terms) by 2 to get rid of the denominator 2. That multiplication
results in the slope intercept form becoming:
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2y = 3x + 4
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Get rid of the 3x on the right side by subtracting 3x from both sides and you have:
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-3x + 2y = 4
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This is the standard form of the answer.
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Hope this helps you to find the source of your error so that you can make a correction.
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