-and-(5-9)-slope.jpeg "(-3 3) And (5 9) Slope")
Understanding Slope: A Comparison of (-3, 3) and (5, 9)
Slope is a fundamental concept in mathematics, particularly in algebra and geometry. It is a measure of how steep a line is, and it can be calculated using the coordinates of two points on the line. In this article, we will explore the slope of two points, (-3, 3) and (5, 9), and understand the concept of slope in the process.
What is Slope?
The slope of a line is a measure of how steep it is. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. Mathematically, it is represented by the symbol "m" and is calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Calculating the Slope of (-3, 3) and (5, 9)
Let's calculate the slope of the line passing through the points (-3, 3) and (5, 9).
Using the slope formula, we get:
m = (9 - 3) / (5 - (-3)) m = 6 / 8 m = 3/4
So, the slope of the line passing through the points (-3, 3) and (5, 9) is 3/4 or 0.75.
Interpreting the Slope
The slope of 3/4 means that for every 4 units we move to the right, the line moves up 3 units. This indicates that the line is rising, but not very steeply.
Comparison of the Two Points
Now, let's compare the slopes of the two points. The point (-3, 3) has a slope of 3/4, while the point (5, 9) has the same slope of 3/4. This means that the line passing through these two points has the same steepness, which is a moderate rise.
Conclusion
In conclusion, we have calculated the slope of the line passing through the points (-3, 3) and (5, 9) and found it to be 3/4. We have also interpreted the slope and compared the two points, finding that they have the same moderate rise. Understanding slope is essential in mathematics, and this article has demonstrated how to calculate and interpret slope using two points.
