You want the point on the graph y = x^2 where the tangent is parallel to the line 2x - y = 2.

Parallel lines have the same slope.

The line given is 2x - y = 2

=> y = 2x - 2

As this is in the form...

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You want the point on the graph y = x^2 where the tangent is parallel to the line 2x - y = 2.

Parallel lines have the same slope.

The line given is 2x - y = 2

=> y = 2x - 2

As this is in the form y = mx + c where m is the slope, the slope of the line is 2.

To find the slope of the tangent at any point on a curve, we need to find the value of the first derivative at that point.

y = x^2

y' = 2x

2x = 2

=> x = 1

y = x^2 = 1

**The required point on the graph at which the tangent is parallel to 2x - y = 2 is (1 , 1).**