Comparing Line A and Line B

Oct 13, 2025 by windailys.com 26 views

Understanding Line Equations and Slope

In mathematics, lines are fundamental geometric shapes used to represent relationships between variables. A line equation is a mathematical expression that describes the relationship between two variables, typically x and y. The slope-intercept form of a line equation is y = mx + b, where m is the slope and b is the y-intercept.

Line A Equation

Line A has the equation y = -4x + 1. This equation represents a line with a slope of -4 and a y-intercept of 1.

Line B Equation

Line B contains the points (-2, 1) and (1, -11). To find the equation of Line B, we need to calculate its slope and y-intercept.

Calculating Slope

The slope of a line can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

Using the given points (-2, 1) and (1, -11), we can calculate the slope of Line B:

m = (-11 - 1) / (1 - (-2)) m = -12 / 3 m = -4

Calculating Y-Intercept

Now that we have the slope, we can use one of the points to calculate the y-intercept. Let's use the point (-2, 1):

1 = -4(-2) + b 1 = 8 + b b = -7

Line B Equation

Now that we have the slope and y-intercept, we can write the equation of Line B:

y = -4x - 7

Comparing Line A and Line B

Let's compare the equations of Line A and Line B:

Line A: y = -4x + 1 Line B: y = -4x - 7

We can see that both lines have the same slope (-4), but different y-intercepts (1 and -7, respectively).

True Statements

Based on the calculations above, we can conclude that:

Line B has a slope of -4.
Line B has a y-intercept of -7.
Line B does not have the same equation as Line A.

Therefore, the true statements are:

Line B has a slope of -4.
Line B has a y-intercept of -7.

Conclusion

Frequently Asked Questions

In this article, we will answer some frequently asked questions related to line equations and slope calculations.

Q: What is the slope-intercept form of a line equation?

A: The slope-intercept form of a line equation is y = mx + b, where m is the slope and b is the y-intercept.

Q: How do I calculate the slope of a line?

A: To calculate the slope of a line, you can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

Q: What is the y-intercept of a line?

A: The y-intercept of a line is the point where the line intersects the y-axis. It is the value of y when x is equal to 0.

Q: How do I calculate the y-intercept of a line?

A: To calculate the y-intercept of a line, you can use the equation:

y = mx + b

where m is the slope and b is the y-intercept. You can substitute the values of m and x into the equation to solve for b.

Q: What is the difference between a line and a curve?

A: A line is a geometric shape that has a constant slope and a single y-intercept. A curve, on the other hand, is a geometric shape that has a variable slope and multiple y-intercepts.

Q: How do I graph a line?

A: To graph a line, you can use the slope-intercept form of the equation and plot two points on the line. You can then draw a line through the two points to represent the line.

Q: What is the equation of a line that passes through two points?

A: To find the equation of a line that passes through two points, you can use the slope formula to calculate the slope of the line, and then use one of the points to calculate the y-intercept.

Q: Can a line have a slope of 0?

A: Yes, a line can have a slope of 0. This means that the line is horizontal and has no y-intercept.

Q: Can a line have a negative slope?

A: Yes, a line can have a negative slope. This means that the line is downward-sloping and has a negative y-intercept.

Q: How do I determine the equation of a line that is parallel to another line?

A: To determine the equation of a line that is parallel to another line, you can use the fact that parallel lines have the same slope. You can then use one of the points on the line to calculate the y-intercept.

Q: How do I determine the equation of a line that is perpendicular to another line?

A: To determine the equation of a line that is perpendicular to another line, you can use the fact that perpendicular lines have slopes that are negative reciprocals of each other. You can then use one of the points on the line to calculate the y-intercept.

Conclusion

In this article, we have answered some frequently asked questions related to line equations and slope calculations. We hope that this article has been helpful in clarifying some of the concepts related to line equations and slope calculations.