Negative slope that goes through the origin is a straight line with a downward slant. It is characterized by its negative slope and its intersection with the origin (0,0). The slope of a line is a measure of its steepness, and a negative slope indicates that the line is decreasing from left to right. Lines with negative slopes are often used to represent decreasing quantities or relationships.
Negative Slope Lines Passing Through the Origin
A line with a negative slope is a line that slopes downward from left to right. When the line passes through the origin (0,0), it means that the line intersects the y-axis at 0 and the x-axis at 0. The equation of a line with a negative slope that passes through the origin is:
y = -mx
where:
- y is the dependent variable (the variable that is being affected)
- x is the independent variable (the variable that is causing the change)
- m is the slope of the line (a negative number)
For example, the line y = -2x is a line with a negative slope of -2 that passes through the origin.
Here are some additional characteristics of lines with negative slopes that pass through the origin:
- The y-intercept of the line is 0.
- The line is in the second quadrant (where both x and y are negative) and the fourth quadrant (where both x and y are positive).
- The line is decreasing from left to right.
- The absolute value of the slope is the rate of change of the line.
Below is a table summarizing the key characteristics of negative slope lines that pass through the origin:
| Characteristic | Value |
|---|---|
| Slope | Negative number |
| Y-intercept | 0 |
| Quadrants | II and IV |
| Direction | Decreasing from left to right |
| Rate of change | Absolute value of the slope |
Question 1:
What is the equation of a line with a negative slope that passes through the origin?
Answer:
The equation of a line with a negative slope that goes through the origin is y = mx, where m is a negative number.
Question 2:
How do you determine the slope of a line that passes through the origin?
Answer:
To determine the slope of a line that passes through the origin, find the change in y and the change in x between any two points on the line. The slope is the ratio of the change in y to the change in x.
Question 3:
What is the y-intercept of a line with a negative slope that passes through the origin?
Answer:
The y-intercept of a line with a negative slope that goes through the origin is 0.
Thanks for sticking with me to the end of this mathematical adventure! I hope you’ve enjoyed learning about the negative slope that goes through the origin. If you have any more questions, feel free to drop me a line. And don’t forget to check back later for more math-related fun and games!