Answer:
[tex]\dfrac{-9}{4}[/tex]
Step-by-step explanation:
All parallel lines have the same slope, so we need to find the slope of the given line. To find the slope of the given line, we will rewrite the equation in slope-intercept form by solving the equation for y. This is y = mx + b, where m is the slope and b is the y-intercept of the line.
Given:
[tex]\displaystyle 9x + 4y = 7[/tex]
Subtract 9x from both sides of the equation:
[tex]\displaystyle 4y = -9x+7[/tex]
Divide both sides of the equation by 4:
[tex]\displaystyle y = \frac{-9}{4} x+\frac{7}{4}[/tex]
The slope of any parallel line to this line will be [tex]\frac{-9}{4}[/tex].
