Problem

Find the slope and y-intercept of the line that passes through the points (1, 3) and (4, 11).

Answer

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Answer

Solving for b, we get: b = 3 - \( \frac{8}{3}\) = -\( \frac{1}{3}\)

Steps

Step 1 ：First, we will use the formula for calculating the slope (m) of a line given two points (x1, y1) and (x2, y2): \(m = \frac{y2-y1}{x2-x1}\)

Step 2 ：Substituting the given points into the formula, we get: \(m = \frac{11-3}{4-1}\) = \( \frac{8}{3}\)

Step 3 ：The y-intercept (b) of a line can be found using the equation of a line: \(y = mx + b\), where m is the slope and (x, y) is a point on the line. Substituting m = \( \frac{8}{3}\), x = 1, and y = 3, we get: 3 = \( \frac{8}{3}\)*1 + b

Step 4 ：Solving for b, we get: b = 3 - \( \frac{8}{3}\) = -\( \frac{1}{3}\)

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