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Write the equation of the line which passes through $(3,5)$ and $(9,9)$. Write the answer in slope-intercept form.
The equation of the line is
(Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
Answer
\(\boxed{y = \frac{2}{3}x + 3}\)
Step 1 ：\(\text{Find the slope: } m = \frac{y_2 - y_1}{x_2 - x_1}\)
Step 2 ：\(m = \frac{9 - 5}{9 - 3} = \frac{4}{6} = \frac{2}{3}\)
Step 3 ：\(\text{Use point-slope form: } y - y_1 = m(x - x_1)\)
Step 4 ：\(y - 5 = \frac{2}{3}(x - 3)\)
Step 5 ：\(\text{Solve for y to get slope-intercept form: } y = mx + b\)
Step 6 ：\(y = \frac{2}{3}x - \frac{2}{3}(3) + 5\)
Step 7 ：\(y = \frac{2}{3}x + 3\)
Step 8 ：\(\boxed{y = \frac{2}{3}x + 3}\)
