\( m=-\frac{4}{5} \), passes through \( (-4,-3) \)

Given that the slope of the line is \( m = -\frac{4}{5} \) and the line passes through the point \((-4, -3)\), we can use the point-slope form of the equation of a line to find the equation of the line. The point-slope form of the equation of a line is given by: \[ y - y_1 = m(x - x_1) \] where \( m \) is the slope of the line and \((x_1, y_1)\) is a point on the line. Substitute the values of \( m = -\frac{4}{5} \) and \((x_1, y_1) = (-4, -3)\) into the point-slope form: \[ y - (-3) = -\frac{4}{5}(x - (-4)) \] \[ y + 3 = -\frac{4}{5}(x + 4) \] Now, simplify the equation to get the final equation of the line. Solve the equation by following steps: - step0: Solve for \(y\): \(y+3=-\frac{4}{5}\left(x+4\right)\) - step1: Multiply the terms: \(y+3=-\frac{4}{5}x-\frac{16}{5}\) - step2: Move the constant to the right side: \(y=-\frac{4}{5}x-\frac{16}{5}-3\) - step3: Subtract the terms: \(y=\frac{-4x-31}{5}\) - step4: Rewrite the fraction: \(y=-\frac{4x+31}{5}\) The equation of the line passing through the point \((-4, -3)\) with a slope of \(-\frac{4}{5}\) is \(y = -\frac{4x+31}{5}\).