Solved Questions on Gradient of a Line
Question 1: Find the gradient of a line which passes through the points (3,5) and (1,4).
Solution:
We know that gradient of a line passing through (x1, y1) and (x2, y2) is given as,
m = (y2-y1)/(x2-x1)
Therefore, gradient or slope of the given line would be,
m = (5-4)/(3-1) = 1/2
Thus, we have calculated the gradient of given line as 1/2.
Question 2: A line makes an angle of 60° with positive X-direction in anticlockwise direction. Find the gradient of line.
Solution:
Here, we have θ = 60° and we know that,
Gradient of a line, m = tan 60° = √3
Thus, gradient of the given line is found to be √3.
Question 3: What is gradient of the line represented as 3x+4y+5=0?
Solution:
We know that,
Slope or Gradient of a line = -(coefficient of x)/(coefficient of y)
Therefore, for given line, we have,
Gradient, m = -3/4
Question 4: Determine the gradient and nature of the curve represented as y = x2 + 5x + 12 at x=2.
Solution:
For any curve, gradient is the slope of tangent line drawn at the given point and it given as dy/dx. Here we have,
y = x2 + 5x + 12
⇒ dy/dx = 2x + 5
At x = 2, dy/dx = 2 × 2 + 5 = 4 + 5 = 9
Thus, a positive value of gradient is obtained which indicates that the function is increasing at x = 2.
Gradient of a Line
Gradient of a Line is the measure of the inclination of the line with respect to the X-axis which is also called slope of a line. It is used to calculate the steepness of a line. Gradient is calculated by the ratio of the rate of change in y-axis to the change in x-axis.
In this article, we will discuss the gradient of a line, methods for its calculation, the gradient of a curve, applications of gradient of a line, some solved examples, and practice problems related to the gradient of a line.
Table of Content
- What is Gradient of a Line?
- How to Calculate Gradient of a Line?
- Gradient of a Curve
- Gradient of Different Lines
- Types of Gradient of a Line