Problem

Find the equation of the line that passes through the points (2,5) and (4,9) using the point-slope form.

Answer

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Answer

Step 3: Simplify the equation to the slope-intercept form (y = mx + b). We have \(y - 5 = 2x - 4\), which simplifies to \(y = 2x + 1\)

Steps

Step 1 ：Step 1: Calculate the slope (m) of the line using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substituting the given points, we get \(m = \frac{9 - 5}{4 - 2} = 2\)

Step 2 ：Step 2: Substitute the slope and one of the points into the point-slope form equation \(y - y_1 = m(x - x_1)\). Using the point (2,5) and the slope 2, we get \(y - 5 = 2(x - 2)\)

Step 3 ：Step 3: Simplify the equation to the slope-intercept form (y = mx + b). We have \(y - 5 = 2x - 4\), which simplifies to \(y = 2x + 1\)

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