Answer:
[tex]y = \frac{ - 3x}{5} + 3[/tex]
Step-by-step explanation:
Change 3x + 5y = 45 to slope intercept form.
[tex]5y = - 3x + 45 \\ \frac{5y}{5} = \frac{ - 3x}{5} + \frac{45}{5} \\ y = \frac{ - 3x}{5} + 9[/tex]
A parallel line has the same slope, therefore, the new equation's slope would be
[tex] \frac{ - 3}{5} [/tex]
Using point slope form
[tex]y - y1 = m(x - x1) \\ y - 6 = \frac{ - 3}{5} (x + 5) \\ y - 6 = \frac{ - 3x}{5} - 3 \\ y = \frac{ - 3x}{5} + 3[/tex]
