For the linear function Y equals 2X minus 8, what is the sum of the X-intercept and the Y-intercept?

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To find the sum of the X-intercept and the Y-intercept for the given linear function ( Y = 2X - 8 ), we first need to determine both intercepts.

The Y-intercept occurs when ( X = 0 ). Substituting this value into the equation gives:

[

Y = 2(0) - 8 = -8.

]

Thus, the Y-intercept is the point ( (0, -8) ).

Next, to find the X-intercept, we set ( Y = 0 ) and solve for ( X ):

[

0 = 2X - 8.

]

Adding 8 to both sides yields ( 2X = 8 ). Dividing both sides by 2 gives us:

[

X = 4.

]

So the X-intercept is the point ( (4, 0) ).

Now, we can sum the X-intercept and the Y-intercept:

[

X\text{-intercept} + Y\text{-intercept} = 4 + (-8) = 4 - 8 = -4.

]

Hence, the sum of the X-intercept and the