• There are two steps to this problem. The first step I'd recommend is finding the slope of the line. You know that the line is perpendicular to the line 3x + 6y = 12. If a line has a slope m, then a line perpendicular to that line has a slope of -1/m. So, find the slope, then take the negative reciprocal. The slope of 3x + 6y = 12 is -1/2, so the slope of a line perpendicular to that line is 2. Next, step is to find a point on the line. If the line intersects with x = y and also x + y = 6, then find the intersection point between those two lines, which is (3,3). Now write the equation for the line with slope 2 that passes through (3,3) in your favourite form.

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