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.

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To find the equation of the line that is perpendicular to a line with a slope of $$ \frac{3}{5} $$ and passes through the point $$ (-3, -4) $$, follow these steps:

1. **Determine the Perpendicular Slope:**
   
   The slope of the perpendicular line is the negative reciprocal of the given slope. 
   
   $$
   m = -\frac{5}{3}
   $$

2. **Use the Point-Slope Form:**
   
   The point-slope form of a line is:
   
   $$
   y - y_1 = m(x - x_1)
   $$
   
   Substituting the known point $$ (-3, -4) $$ and the slope $$ m = -\frac{5}{3} $$:
   
   $$
   y - (-4) = -\frac{5}{3}(x - (-3))
   $$
   
   Simplifying:
   
   $$
   y + 4 = -\frac{5}{3}(x + 3)
   $$

3. **Convert to Slope-Intercept Form:**
   
   Distribute the slope on the right-hand side:
   
   $$
   y + 4 = -\frac{5}{3}x - 5
   $$
   
   Subtract 4 from both sides to solve for $$ y $$:
   
   $$
   y = -\frac{5}{3}x - 9
   $$

**Final Equation:**
$$
y = -\frac{5}{3}x - 9
$$
The equation of the line in slope-intercept form is $$ y = -\frac{5}{3}x - 9 $$.

A line contains the point and is perpendicular to a line with a slope of .
Write an equation of the line satisfying the given conditions. Write the answer in
slope-intercept form.

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A line contains the point and is perpendicular to a line with a slope of . Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form.