A line contains the point \( (-3,-4) \) and is perpendicular to a line with a slope of \( { }^{\frac{3}{5}} \). Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form.

To find the equation of the line that contains the point \( (-3,-4) \) and is perpendicular to a line with a slope of \( \frac{3}{5} \), you first need to determine the slope of the new line. Since perpendicular lines have slopes that multiply to \(-1\), you can find the slope (m) of the line you want by using the formula: \[ m \cdot \frac{3}{5} = -1 \] Solving for \( m \) gives: \[ m = -\frac{5}{3} \] Now, you can use the point-slope form of the equation of a line, which is: \[ y - y_1 = m(x - x_1) \] Substituting in the point \( (-3, -4) \) and the slope \( -\frac{5}{3} \): \[ y - (-4) = -\frac{5}{3}(x - (-3)) \] Simplifying that gives: \[ y + 4 = -\frac{5}{3}(x + 3) \] Distributing the slope: \[ y + 4 = -\frac{5}{3}x - 5 \] Now, isolate \( y \): \[ y = -\frac{5}{3}x - 5 - 4 \] This simplifies to: \[ y = -\frac{5}{3}x - 9 \] Thus, the equation of the line in slope-intercept form is: \[ y = -\frac{5}{3}x - 9 \] This is your final answer!