SOLUTION: 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). I

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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

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).

You can put this solution on YOUR website!
Let's take this a step at a time:
You want a line parallel to 2x+4y =9. So the first thing you have to know is lines that are parallel have the SAME slope.
Therefore, you have to find the slope for the equation, 2x + 4y = 9. How can you do that?

Let's change the equation to the y = mx + b format (the slope intercept form of a line) where "m" is the slope. If we want to put the equation into y = mx + b format, we have to solve for "y". SO here goes:

2x+ 4y = 9 (your original equation)
4y = -2x + 9 (subtracted 2x from both sides to isolate the y)
y = + (divided both sides by 4 to isolate the y)

y = + (simplified the fraction of to )


Now we can see that the slope of the line is }. Therefore, any line parallel to that line must ALSO have a slope of .

Now to the next step:

Your new line must also go thru the point (6, -2)

When you know the point that a line must go thru and the slope you want, then you just "plug" this info into the point/slope form of a line. The point slope form of a line is:

=


SO let's plug in our info:
We want a slope of and we want it to go thru point (6, -2)

y - -2 = (x - 6)

y - -2 is really y + 2 so let's rewrite the above and then do the math.

y + 2 = (x - 6) If your teacher wants the answer in "point/slope" form, you are finished at this step. If the teacher wants the answer in slope/intercept form, then you have to do more thinking. You'd have to do this:

y + 2 = (x - 6) (equation in point/slope form)
y + 2 = + 3 (distributed )
y = + 3 - 2 (subtracted 2 from both sides of the equation)
y = + 1 (equation in slope intercept form)

I think that's everything. I hope it helps you and good luck on your final. :-)