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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

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Answer

$y = \frac{2}{3} x + 3$

Steps

Step 1 ： $Find the slope: m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 2 ： $m = \frac{9 - 5}{9 - 3} = \frac{4}{6} = \frac{2}{3}$

Step 3 ： $Use point-slope form: y - y_{1} = m (x - x_{1})$

Step 4 ： $y - 5 = \frac{2}{3} (x - 3)$

Step 5 ： $Solve for y to get slope-intercept form: y = m x + b$

Step 6 ： $y = \frac{2}{3} x - \frac{2}{3} (3) + 5$

Step 7 ： $y = \frac{2}{3} x + 3$

Step 8 ： $y = \frac{2}{3} x + 3$