What is an equation of the line that passes through the point \( (-4,-3) \) and is parallel to the line \( 5 x-2 y=12 \) ?

To find the equation of a line that is parallel to a given line, we first need to determine the slope of the line represented by the equation \( 5x - 2y = 12 \). We can rearrange this into slope-intercept form (y = mx + b). Starting with the given equation: \[ 5x - 2y = 12 \] Rearranging gives: \[ -2y = -5x + 12 \] \[ y = \frac{5}{2}x - 6 \] The slope (m) of the line is \( \frac{5}{2} \). Lines that are parallel have the same slope. Now that we know our new line must have a slope of \( \frac{5}{2} \) and passes through the point \( (-4, -3) \), we can use the point-slope form of the equation. Using the point-slope form: \[ y - y_1 = m(x - x_1) \] Substituting \( m = \frac{5}{2} \), \( x_1 = -4 \), and \( y_1 = -3 \): \[ y - (-3) = \frac{5}{2}(x - (-4)) \] \[ y + 3 = \frac{5}{2}(x + 4) \] Now simplify: \[ y + 3 = \frac{5}{2}x + 10 \] \[ y = \frac{5}{2}x + 7 \] So, the equation of the line that passes through the point \( (-4, -3) \) and is parallel to the line \( 5x - 2y = 12 \) is: \[ y = \frac{5}{2}x + 7 \]