Problem

Given the points A(2,4) and B(6,8), find the slope and y-intercept of the line AB.

Answer

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Answer

To find the y-intercept (b), we use the formula \(b = y - mx\), where m is the slope and (x, y) is a point on the line. Substituting the slope and the coordinates of point A, we get \(b = 4 - 1*2 = 2\).

Steps

Step 1 ：To find the slope (m) of the line AB, we use the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points. Substituting the given coordinates, we get \(m = \frac{8-4}{6-2} = 1\).

Step 2 ：To find the y-intercept (b), we use the formula \(b = y - mx\), where m is the slope and (x, y) is a point on the line. Substituting the slope and the coordinates of point A, we get \(b = 4 - 1*2 = 2\).

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