Example on Slope Formula
Example 1: Find the slope of a line whose coordinates are (3, 7) and (5, 8).
Solution:
Given, (x1, y1) = (3,7) and (x2, y2) = (5,8)
Slope formula (m) = (y2 – y1)/(x2 – x1)
⇒ m = (8 – 7)/(5 – 3) = 1/2
Hence, the slope of the given line is 1/2.
Example 2: Determine the slope of a line whose coordinates are (7, -5) and (2, -3).
Solution:
Given, (x1, y1) = (7, -5) and (x2, y2) = (2, -3)
Slope formula (m) = (y2 – y1)/(x2 – x1)
⇒ m = (-3 – (-5))/(2 – 7) = -2/5
Hence, the slope of the given line is -2/5
Example 3: Find the value of a, if the slope of a line passing through the points (-4, a) and (2, 5) is 3.
Solution:
Given, (x1, y1) = (4,a) and (x2, y2) = (2, 5) and slope (m) = 3
We know that slope (m) = (y2 – y1)/(x2 – x1)
⇒ 3 = (5 – a)/(2 – 4)
⇒ 3 = (5 – a)/(-2)
⇒ -6 = 5 – a ⇒ a = 5 + 6 = 11
Hence, the value of a = 11
Example 4: If a line makes an angle of 60° with the positive Y-axis, then what is the value of the slope of the line?
Solution:
Given data, Angle made by a line with the positive y-axis = 60°
We know that if the line makes an angle of 60° from the positive y-axis, then it makes an angle of (90° – 60° = 30°) with the x-axis.
Therefore, the value of the slope of the line (m) = tan 30° = 1/√3
Hence, the value of the slope of the line = 1/√3.
Example 5: Sheela was checking a graph, and she noticed that the raise was 12 units and the run was 4 units. Now calculate the slope of a line.
Solution:
Given data, rise = 12 units and run = 4 units
We know that slope (m) = rise/run
⇒ m = 12/4 = 3
Hence, the slope of the given line is 3
Example 6: Find the slope of the line 3x – 7y + 8 = 0.
Solution:
Given data, The equation of the line = 3x – 7y + 8 = 0
Now, compare the given with the general equation of the line i.e., ax + by + c = 0
Therefore, a = 3, b = -7 and c = 8
We know that Slope (m) = – coefficient of x/coefficient of y = -a/b
⇒ m = -3/(-7) = 3/7
Hence, the slope of the given line is 3/7.
Slope Formula
Slope formula is used to determine the steepness or inclination of a line. The x and y coordinates of the points lying on the line are used to calculate the slope of a line. The change in the “y” coordinate concerning the change in the “x” coordinates is called the slope of a line, and it is usually depicted by the letter “m”.
Table of Content
- What is Slope Formula?
- Slope Formula
- Derivation of Slope Formula
- Slope of a Line (Straight Line) Formula
- Slope Equation
- Example on Slope Formula