Understanding the Basics of Slope and Parallel Lines

Oct 13, 2025 by miodeya.com 136 views

What is the Slope of a Line Parallel to the Line $9x + 4y = 7$ ?

Understanding the Basics of Slope and Parallel Lines

In mathematics, the slope of a line is a fundamental concept that helps us understand the steepness or incline of a line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The slope of a line is denoted by the letter 'm' and is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Parallel lines are lines that lie in the same plane and never intersect, no matter how far they are extended. In other words, parallel lines have the same slope but different y-intercepts. If two lines are parallel, their slopes are equal, and their equations can be written in the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Finding the Slope of the Given Line

To find the slope of a line parallel to the line $9x + 4y = 7$ , we need to first convert the given equation into the slope-intercept form, y = mx + b. To do this, we need to isolate the variable 'y' on one side of the equation.

Rearranging the equation $9x + 4y = 7$ , we get:

4y = -9x + 7

Dividing both sides of the equation by 4, we get:

y = (-9/4)x + 7/4

Now that we have the equation in the slope-intercept form, we can see that the slope of the line is -9/4.

Finding the Slope of a Line Parallel to the Given Line

Since parallel lines have the same slope, the slope of a line parallel to the line $9x + 4y = 7$ is also -9/4.

Conclusion

In conclusion, the slope of a line parallel to the line $9x + 4y = 7$ is -9/4. This is because parallel lines have the same slope, and the slope of the given line is -9/4.

Answer

The correct answer is B. ${$ -\frac{9}{4}$}$.

Additional Information

The slope of a line is a measure of its steepness or incline.
Parallel lines have the same slope but different y-intercepts.
The slope of a line can be calculated using the formula: m = (y2 - y1) / (x2 - x1).
The slope-intercept form of a line is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Frequently Asked Questions

What is the slope of a line parallel to the line $9x + 4y = 7$ ?
How do you find the slope of a line parallel to a given line?
What is the slope-intercept form of a line?
How do you calculate the slope of a line using the formula: m = (y2 - y1) / (x2 - x1)?

References

[1] Khan Academy. (n.d.). Slope of a line. Retrieved from https://www.khanacademy.org/math/algebra/x2f6f6c/slope-of-a-line/v/slope-of-a-line
[2] Math Open Reference. (n.d.). Slope of a line. Retrieved from https://www.mathopenref.com/slope.html
[3] Purplemath. (n.d.). Slope of a line. Retrieved from https://www.purplemath.com/modules/slope.htm