Answer: [tex]y=-\frac{7}{4}x-\frac{3}{4}[/tex]
Step-by-step explanation:
Rearranging the line into slope-intercept form,
[tex]4y+7x=-6\\\\4y=-7x-6\\\\y=-\frac{7}{4}x-\frac{3}{2}[/tex]
Since the center of dilation does not lie on the line, we can multiply the y-intercept by the scale factor of the dilation.
So, the equation of the line is [tex]y=-\frac{7}{4}x-\frac{3}{4}[/tex]
