Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through \( (-4,-5) \) and \( (1,5) \) What is the equation of the line in point-slope form? \( \square \) (Simplify your answer. Use integers or fractions for any numbers in the equation.)

To find the equation of the line passing through the points \((-4, -5)\) and \( (1, 5)\), we first need to determine the slope (m). The slope is given by the formula \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-5)}{1 - (-4)} = \frac{10}{5} = 2. \] Now that we have the slope, we can use point-slope form \(y - y_1 = m(x - x_1)\). Using either point, let's use \((-4, -5)\): \[ y - (-5) = 2(x - (-4)), \] which simplifies to: \[ y + 5 = 2(x + 4). \] For slope-intercept form \(y = mx + b\), we can convert the obtained point-slope equation: 1. Distribute \(2\): \[ y + 5 = 2x + 8. \] 2. Subtract \(5\) from both sides: \[ y = 2x + 3. \] In conclusion, the equation of the line in point-slope form is \[ y + 5 = 2(x + 4) \] and in slope-intercept form is \[ y = 2x + 3. \]