Find an equation for the line below \( (-4,3)(6,-3) \)

To find the equation of the line that passes through the points \((-4,3)\) and \((6,-3)\), we can use the point-slope form of a linear equation: \[ y - y_1 = m(x - x_1) \] where \( m \) is the slope of the line and \( (x_1, y_1) \) is one of the points on the line. First, let's find the slope \( m \) using the two given points: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates of the points: \[ m = \frac{-3 - 3}{6 - (-4)} \] \[ m = \frac{-6}{6 + 4} \] \[ m = \frac{-6}{10} \] \[ m = -\frac{3}{5} \] Now that we have the slope, we can use either of the two points to write the equation in point-slope form. Let's use the point \((-4,3)\): \[ y - 3 = -\frac{3}{5}(x - (-4)) \] \[ y - 3 = -\frac{3}{5}(x + 4) \] To get the equation in slope-intercept form \( y = mx + b \), we can distribute the slope and simplify: \[ y - 3 = -\frac{3}{5}x - \frac{3}{5} \cdot 4 \] \[ y - 3 = -\frac{3}{5}x - \frac{12}{5} \] Now, add 3 to both sides to isolate \( y \): \[ y = -\frac{3}{5}x - \frac{12}{5} + 3 \] \[ y = -\frac{3}{5}x - \frac{12}{5} + \frac{15}{5} \] \[ y = -\frac{3}{5}x + \frac{3}{5} \] So, the equation of the line in slope-intercept form is: \[ y = -\frac{3}{5}x + \frac{3}{5} \]