Write the point-slope form of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation. Passing through \( (1,3) \) and \( (2,6) \) Type the point-slope form of the equation of the line. Thimplify your answer. Use integers or fractions for any number in the equation.) Type the-intercept form of the equation of the line. (Simplify your answer. Use integers or fractions for any number in the equation.)

To find the equation of the line passing through the points \( (1, 3) \) and \( (2, 6) \), we'll follow these steps: 1. **Determine the slope (m):** \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 3}{2 - 1} = \frac{3}{1} = 3 \] 2. **Write the point-slope form:** Using the point \( (1, 3) \) and the slope \( m = 3 \): \[ y - y_1 = m(x - x_1) \\ y - 3 = 3(x - 1) \] 3. **Simplify to slope-intercept form:** Expand and simplify the equation: \[ y - 3 = 3x - 3 \\ y = 3x \] **Final Answers:** - **Point-Slope Form:** \[ y - 3 = 3(x - 1) \] - **Slope-Intercept Form:** \[ y = 3x \]