Slope Calculation Between Two Points
The slope of a line measures its steepness and direction. We calculate it using the coordinates of two distinct points on the line.
Let the two points be $(x_1, y_1)$ and $(x_2, y_2)$. The formula for the slope ($m$) is:
$ m = \frac{y_2 - y_1}{x_2 - x_1} $
Given the points are $(-2, 5)$ and $(4, -7)$. We assign:
- $x_1 = -2$
- $y_1 = 5$
- $x_2 = 4$
- $y_2 = -7$
Substitute these values into the slope formula:
$ m = \frac{-7 - 5}{4 - (-2)} $
Calculate the numerator (the change in y):
$ -7 - 5 = -12 $
Calculate the denominator (the change in x):
$ 4 - (-2) = 4 + 2 = 6 $
Now, divide the change in y by the change in x:
$ m = \frac{-12}{6} $
$ m = -2 $
Thus, the slope of the line passing through the points $(-2, 5)$ and $(4, -7)$ is $-2$.
Similar Questions
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Important Questions from Coordinate Geometry
What is the reflection of the point (-1, 5) in the line x = 1?
What are the co-ordinates of the centroid of a triangle, whose vertices are A(1, -5), B(-4, 0) and C(3, -4)?
Slope of the line AB is 4/3. Co-ordinates of points A and B are (x, -5) and (2, -3) respectively. What is the value of x?
Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).
- If x² + y² - 12x + 18y + 117 = 0, then the value of x² + y² is:
