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Question 250242: I am having trouble with how to find the equation of the line.
Here is the problem:
Find the equation of the line parallel to 2x+4y=9 and passing through the point (6,-2).
If someone could walk me through the steps on how to find the answer i would really appreciate it i have a final in two days!
Found 3 solutions by solver91311, Theo, PRMath:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
In point of fact, you cannot do what you ask to be done. You cannot find "the" equation of any line. That is because there are an infinite number of equations that represent any given line. What you can do is find "an" equation that fits the given parameters. Herewith the method:
Step 1: Solve the given equation for  in terms of everything else. In other words, put the given equation into slope-intercept form, 
Step 2: Use the fact that parallel lines have equal slopes, which is to say:
to determine the slope of the desired line by inspection of the coefficient on  in the slope-intercept form equation that resulted from the completion of step 1.
Step 3: Use the point-slope form, the coordinates of the given point, and the slope determined in Step 2 to write an equation of the desired line.
 )
where ) are the coordinates of the given point and  is the slope.
Step 4: If necessary, either because the problem instructions require it, or because you need to have the equation in a particular form in order to use it in a subsequent calculation, rearrange the equation into an appropriate form. Two very common form requirements are slope-intercept form (shown in step 1 of this procedure) and Standard Form,  . Note: Some texts require that A, B, and C be integers for proper standard form.
John
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! convert the equation to slope-intercept form.
the slope-intercept form of a straight line is y = mx + b where m is the slope and b is the y-intercept.
2x + 4y = 9 is the equation.
subtract 4x from both sides of the equation to get:
4y = -2x + 9
divide both sides of the equation by 4 to get:
y = (-2/4)x + (9/4)
that's the slope intercept of the line.
the slope is (-2/4) which is the same as (-1/2).
the equation becomes:
y = (-1/2)x + (9/4)
the line parallel to this line will have the same slope.
the equation for that line starts out as:
y = (-1/2)x + b
take your point of (x,y) = (6,-2) and substitute for x and y in this equation to get:
-2 = (-1/2)*6 + b
simplify to get:
-2 = -3 + b
add 3 to both sides of this equation to get:
-2 + 3 = b
combine like terms to get:
1 = b
equation of line parallel to your line is:
y = (-1/2)x + 1
you have 2 equations that are parallel to each other.
those equations are:
y = (-1/2)x + (9/4) and y = (-1/2)x + 1
graph of the equations of these lines is shown below:
you can see that the equation of y = (-1/2)x + (9/4) crosses the y-axis at about y = 2.25 which is where it would cross when x = 0.
you can see that the equation of y = (-1/2)x + 1 crosses the y-axis at about y = 1 which is where it would cross when x = 0.
you can see that the equation of y = (-1/2)x + 1 goes through the point (x,y) = (6,-2).
Answer by PRMath(133)  (Show Source):
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