Use the given conditions to write an equation for the line in point-slope form and slope-mntercept form Passing through \( (-3,-2) \) and \( (3,6) \) Type the point-slope form of the equation of the line \( \square \) Use integers or simplified fractions for any numbers in the equation ) (Un)

To find the equation of the line passing through the points \((-3, -2)\) and \((3, 6)\), follow these steps: ### 1. Calculate the Slope (\(m\)) The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the given points: \[ m = \frac{6 - (-2)}{3 - (-3)} = \frac{8}{6} = \frac{4}{3} \] ### 2. Point-Slope Form The **point-slope form** of a line is: \[ y - y_1 = m(x - x_1) \] Using the point \((-3, -2)\) and the slope \( \frac{4}{3} \): \[ y - (-2) = \frac{4}{3}(x - (-3)) \] Simplifying: \[ y + 2 = \frac{4}{3}(x + 3) \] **Point-Slope Form Equation:** \[ \boxed{y + 2 = \dfrac{4}{3}(x + 3)} \] ### 3. Slope-Intercept Form The **slope-intercept form** of a line is: \[ y = mx + b \] Using the slope \( \frac{4}{3} \) and one of the points to solve for \(b\). Let's use \((3, 6)\): \[ 6 = \frac{4}{3}(3) + b \\ 6 = 4 + b \\ b = 2 \] **Slope-Intercept Form Equation:** \[ y = \frac{4}{3}x + 2 \]