Problem

Find the equation of the line that passes through the points (3,7) and (6,13).

Answer

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Answer

Step 3: Simplifying the above equation, we get \(y - 7 = 2x - 6\), or equivalently, \(y = 2x + 1\).

Steps

Step 1 ：Step 1: We know that the slope of a line is given by the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). So, we substitute the given points into this formula to find the slope: \(m = \frac{13 - 7}{6 - 3} = 2\).

Step 2 ：Step 2: Now, we can use the point-slope form of a linear equation, which is \(y - y_1 = m(x - x_1)\). Substituting one of the given points and the slope into this equation, we get \(y - 7 = 2(x - 3)\).

Step 3 ：Step 3: Simplifying the above equation, we get \(y - 7 = 2x - 6\), or equivalently, \(y = 2x + 1\).

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