Problem

Find the equation of the line that passes through the point (3,5) and has a slope of 2.

Answer

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Answer

Finally, add 5 to both sides to solve for y, yielding the equation \(y = 2x - 1\).

Steps

Step 1 ：The point-slope form of a line is given by \(y - y_1 = m(x - x_1)\), where \(m\) is the slope of the line and \((x_1, y_1)\) is a point on the line.

Step 2 ：Given the point (3,5) and the slope 2, we can substitute these values into the point-slope form to get \(y - 5 = 2(x - 3)\).

Step 3 ：Distribute the 2 on the right side of the equation to get \(y - 5 = 2x - 6\).

Step 4 ：Finally, add 5 to both sides to solve for y, yielding the equation \(y = 2x - 1\).

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