Problem

This quiz: 10 point(s) possible This question: 1 point(s) possible Resume later Submit quiz 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.)

Solution

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 :\(\boxed{y = \frac{2}{3}x + 3}\)

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Source: https://solvelyapp.com/problems/15530/

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