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Slope Formula
Understanding the Steepness of a Line
The slope formula is used to calculate the steepness or the incline of a line. The x and y coordinates of the lines are used to calculate the slope of the line. It is the ratio of the change in the y-axis to the change in the x-axis.
Formula of Slope
The formula to calculate slope is given as:
m = (y2 − y1) / (x2 − x1)
Where m is the slope of the line. x1, x2 are the coordinates of the x-axis, and y1, y2 are the coordinates of the y-axis.
Sample Examples
Question 1:
Find the slope of a line whose coordinates are (2, 7) and (8, 1)?
Solution:
Given,
(x1, y1) = (2, 7)
(x2, y2) = (8, 1)
The slope formula is:
m = (y2 − y1) / (x2 − x1)
Calculations:
m = (1 − 7) / (8 − 2)
m = −6 / 6
m = −1
Question 2:
If the slope of a line passing through the points (4, b) and (2, -9) is 3, then what is the value of b?
Solution:
Given,
Slope = m = 3
Points:
(x1, y1) = (4, b)
(x2, y2) = (2, -9)
Using the slope formula:
m = (y2 – y1) / (x2 – x1)
Since the slope is 3:
3 = (-9 – b) / (2 – 4)
3 = (-9 – b) / (-2)
-9 – b = 3(-2)
-9 – b = -6
b = -9 + 6 = -3
Therefore, the value of b is -3.