The slope of any line parallel to the given line can be found by rearranging the equation into the slope-intercept form, which is y = mx + b, where m represents the slope.
Let’s start with the given equation:
9x + 4y = 7
We want to isolate y by moving 9x to the other side:
4y = -9x + 7
Now, divide every term by 4 to solve for y:
y = - rac{9}{4}x + rac{7}{4}
From this equation, we can see that the slope (m) of the line is - rac{9}{4}.
Since parallel lines have the same slope, any line parallel to the line 9x + 4y = 7 will also have a slope of - rac{9}{4}.