Write an equation in the variables x and y for the line that passes through the point (4, 7) and that is perpendicular to the line 2x + 2y = 14. provide precise expressions, not decimal approximations.

First of all, we need to find the slope of the given line, writing it in the form and reading the coefficient:

So, the slope is

If a line with slope is perpendicular to a line with slope , the following relationship holds:

So, the slope of our line must satisfy

So, we need the equation of a line with slope 1 and passing through (4,7). Given the slope and a point of a given line, its equation is given by

So, if you plug your values, you have

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step-by-step explanation:

step-by-step explanation: