To determine the slope of any line that is parallel to the line defined by the equation 9x + 4y = 7, we first need to express this equation in the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Here’s a step-by-step breakdown:
- Start with the original equation: 9x + 4y = 7.
- Isolate the term with y on one side:
- Subtract 9x from both sides: 4y = 7 – 9x.
- Now, divide every term by 4 to solve for y:
- y = - rac{9}{4}x + rac{7}{4}.
In this equation, the slope (m) is - rac{9}{4}. Lines that are parallel to each other have the same slope, meaning that any line parallel to the line represented by 9x + 4y = 7 will also have a slope of - rac{9}{4}.
In summary, the slope of any line parallel to the line defined by the equation 9x + 4y = 7 is - rac{9}{4}.