Step-by-step explanation:
Paralle lines have the same slope.
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have
[tex]5y+9=-2x[/tex]
Convert to the slope-intercept form:
[tex]5y+9=-2x[/tex] subtract 9 from both sides
[tex]5y=-2x-9[/tex] divide both sides by 5
[tex]y=-\dfrac{2}{5}x-\dfrac{9}{5}\to m=-\dfrac{2}{5}[/tex]
Each of the answers to choose from is not the line equation sought.
The equation:
[tex]y=-\dfrac{2}{5}x+b[/tex] where b is any real number.
