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graph -1/2x + 1/6y = 2/3

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2 Answers

Was not sure if you meant -1/(2x)+ 1/(6y) = 2/3 or (-1/2)x + (1/6)y = 2/3

The solution for -1/(2x)+ 1/(6y) = 2/3 is as follows:

-1/(2x) + 1/(6y) = 2/3

could be rewritten as follows by adding 1/(2x) to both sides of the equation.

-1/(2x) + 1/(2x) + 1/(6y) = 2/3 + 1/(2x)

1/(6y) = 1/(2x) + 2/3.

Now we add the components on the right side with common denominator

1/(6y) = (3 + 4x)/(6x)

which can be further simplified as follows

1/y = (3 + 4x)/x

Now we have to find the multiplicative inverses on both sides. That is,

y = x/ (3 + 4x) or y = x/ (4x + 3)

Now to plot a graph, we have to find the ordered pairs or the co-ordinates of the points and then join them.

For eg: when x= 0, y= 0; x= 3, y= 3/15 or 1/5; we have ordered pairs and they are P1 (0,0) and P2 (3,1/5). P1 and P2 can be connected.

Before graphing a linear equation, it is usually best to change the equation into slope-intercept form.To find the slope intercept form of the line, we need to solve the equation for y.  I am assuming that the terms are -1/2 times x and 1/6 times y, not -1 over 2x and 1 over 6y.

-1/2x + 1/6y = 2/3                            Given

-1/2x + 1/6y + 1/2x = 2/3 + 1/2x       Add 1/2x to each side

1/6y = 1/2x + 2/3                            Simplify

6(1/6y) = 6(1/2x + 2/3)                   Multiply each side by 6

6(1/6y) = 6/2x + 6(2)/3                   Distribute the 6

y = 3x + 4                                      Simplify

In slope-intercept form, the value added to x is called the y-intercept.  When x = 0, then y equals the number (in this case, the number is 4).  That means you need to plot a point at (0,4).

The number multiplied by x is the slope.  In this problem, the slope is 3.  That means that you should count 3 places up from you point for each 1 place counted to the right.  You should come to the point (1,7).  Plot a point here.

Once you have two points plotted, use a straight edge to draw your line through the points.  You now have the graph of the equation.



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