What is the x and y intercept for the equation: 1/3x - 1/6y = -2/3
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We first need to re-arrange the equation into slope-intercept form (RECALL: y = mx + b)
-1/6y = -1/3x - 2/3
Now, multiply both sides by -6 to isolate the y variable. (RECALL: multiplication of fractions
is multiplying across the top and across the bottom. In this case, -6 is same as -6/1 so ignore the bottom since multiplication by 1 is the other number)
-6*(-1/6y) = -6*(-1/3x - 2/3)
6/6y = 6/3x + 12/3 (be mindful of sign changes)
We simplify the last step to get:
y = 2x + 4
It is now in the form:
y = mx + b
y-intercept is where x=0
y = 2(0) + 4
y = 4
Y-Intercept is (0,4)
x-intercept is where y=0
0 = 2x + 4
-4 = 2x
-2 = x
X-Intercept is (-2,0)
-1/6y = -1/3x - 2/3
Now, multiply both sides by -6 to isolate the y variable. (RECALL: multiplication of fractions
is multiplying across the top and across the bottom. In this case, -6 is same as -6/1 so ignore the bottom since multiplication by 1 is the other number)
-6*(-1/6y) = -6*(-1/3x - 2/3)
6/6y = 6/3x + 12/3 (be mindful of sign changes)
We simplify the last step to get:
y = 2x + 4
It is now in the form:
y = mx + b
y-intercept is where x=0
y = 2(0) + 4
y = 4
Y-Intercept is (0,4)
x-intercept is where y=0
0 = 2x + 4
-4 = 2x
-2 = x
X-Intercept is (-2,0)
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6*[1/3x - 1/6y = -2/3]
2x - y = -4 ---> y = 2x+4
for x intercept, take y=0. Then you have 2x+2 = 0 --> 2x = -2 --> x = -1
Thus the y intercept is 4 and the x intercept is -1.
Alternatively, just evaluate the original function at x = 0 to get -1/6y = -2/3 --> y = 4
and y=0 to get 1/3x = -2/3 --> x = -1
2x - y = -4 ---> y = 2x+4
for x intercept, take y=0. Then you have 2x+2 = 0 --> 2x = -2 --> x = -1
Thus the y intercept is 4 and the x intercept is -1.
Alternatively, just evaluate the original function at x = 0 to get -1/6y = -2/3 --> y = 4
and y=0 to get 1/3x = -2/3 --> x = -1
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Well...x & y intercepts are the x & y coordinates of a graph right...
So why don't we use the cover up method. The cover up method is
when you cover up one of the variables and start from that equation.
For example: 2x+4y=12
All we do is take a thumb and cover one of the #'s/variables, so
the 2 separate equations would be:2x=12 and 4y=12
Now divide 12 by both #'s to get: 6x & 3y
Now put the two into an ordered pair/coordinate:
X-intercept=(6,0) Y-intercept=(0,3)
Now let's do ur math problem.
1/3x-1/6y=-2/3
Using the cover up method our 2 equations are:
1/3x=-2/3 & -1/6y=-2/3
Now divide -2/3 by our #'s/variables to get:
-2x & 4
Now we put them into ordered pairs/coordinates to get the ANSWER:
x-intercept= (-2,0) y-intercept=(0,4)
Hint: -2 goes into the x spot because it's the X intercept...same goes for Y-intercept
Hint#2: If X-intercept the Y is always 0....if Y intercept the X is always 0.
I hope this helps u :)
If you need more help/practice go to:
http://www.khanacademy.org/
So why don't we use the cover up method. The cover up method is
when you cover up one of the variables and start from that equation.
For example: 2x+4y=12
All we do is take a thumb and cover one of the #'s/variables, so
the 2 separate equations would be:2x=12 and 4y=12
Now divide 12 by both #'s to get: 6x & 3y
Now put the two into an ordered pair/coordinate:
X-intercept=(6,0) Y-intercept=(0,3)
Now let's do ur math problem.
1/3x-1/6y=-2/3
Using the cover up method our 2 equations are:
1/3x=-2/3 & -1/6y=-2/3
Now divide -2/3 by our #'s/variables to get:
-2x & 4
Now we put them into ordered pairs/coordinates to get the ANSWER:
x-intercept= (-2,0) y-intercept=(0,4)
Hint: -2 goes into the x spot because it's the X intercept...same goes for Y-intercept
Hint#2: If X-intercept the Y is always 0....if Y intercept the X is always 0.
I hope this helps u :)
If you need more help/practice go to:
http://www.khanacademy.org/