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find the x-intercept and the y-intercept of 1/2x-2y=4

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2 Answers

The intercepts of any equation are where the line crosses that axis.  For an x-intercept the coordinate point would look something like (x,0), for any value of x. The y value would have to be zero to intercept the x-axis. The same for the y-intercept, it would look like (0,y) because the x value would have to equal zero.
 
So to solve your problem substitute zero in for the x value first and solve for y. That would give you:
 
1/2(0) - 2y = 4
0 - 2y = 4
-2y = 4
y=-2
 
So y equals -2 when x equals 0. Your coordinate would be (0,-2), that's your y-intercept.
 
Same thing for the x-intercept, we can find that value by substituting 0 for y:
1/2x - 2(0) = 4
1/2x - 0 = 4
1/2x = 4
x=8
 
So x equals 8 when y equals 0. Your coordinate would be (8,0), that's your x-intercept.
To find the X-intercept, plug 0 in for Y and solve.


1/2X - 2Y = 4
1/2X - 2(0) = 4
1/2X = 4
X = 4*2
X= 8
Because we plugged 0 in for Y, the coordinate is (8,0)

To find the Y-intercept, plug 0 in for X and solve.

1/2X - 2Y = 4
(1/2)(0) - 2Y = 4
-2Y = 4
Y = 4/-2
Y = -2
Because we plugged 0 in for X, the coordinate is (0, -2)

X-Intercept = (8, 0); Y-Intercept = (0, -2)

It may help you to check your answer if you see it visually by graphing the equation.