Find the equation in slope-intercept form for the line passing through the points with the given coordinates. \[ (1,3),(-2,-1) \]

To find the equation of the line in slope-intercept form \( y = mx + b \) that passes through the points \( (1, 3) \) and \( (-2, -1) \), follow these steps: 1. **Calculate the slope (\( m \))**: The slope \( m \) is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the given points: \[ m = \frac{-1 - 3}{-2 - 1} = \frac{-4}{-3} = \frac{4}{3} \] 2. **Find the y-intercept (\( b \))**: Use one of the points and the slope to solve for \( b \). Let's use the point \( (1, 3) \): \[ 3 = \frac{4}{3}(1) + b \\ 3 = \frac{4}{3} + b \\ b = 3 - \frac{4}{3} = \frac{9}{3} - \frac{4}{3} = \frac{5}{3} \] 3. **Write the equation in slope-intercept form**: \[ y = \frac{4}{3}x + \frac{5}{3} \] **Final Answer:** \[ y = \dfrac{4}{3}\,x\;+\;\dfrac{5}{3} \]