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What is the equation of the line that passes through the point $(6,2)$ and has a slope of $\frac{1}{3}$ ?
Answer Attempt 3 out of 3
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\(\boxed{The equation of the line is y = \frac{1}{3}x + 0, or simply y = \frac{1}{3}x}\).
Step 1 ：The equation of a line in slope-intercept form is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Step 2 ：We are given the slope \(m = \frac{1}{3}\) and a point \((x_1, y_1) = (6, 2)\). We can substitute these values into the equation to solve for \(b\).
Step 3 ：Substituting the values, we get \(2 = \frac{1}{3} * 6 + b\). Solving for \(b\), we find that \(b = 0\).
Step 4 ：Now that we have the y-intercept \(b = 0\), we can write the equation of the line.
Step 5 ：\(\boxed{The equation of the line is y = \frac{1}{3}x + 0, or simply y = \frac{1}{3}x}\).
