The gradient of a line refers to the steepness or slope of that line. It is a measure of its slope.
Understanding the different types of gradients is crucial when working with lines and their equations. Depending on the value of the gradient, there are four different types of gradient positive, negative, zero and undefined.
2. Negative gradients: A line with a negative gradient has a slope that goes down from left to right, and the value of the gradient is less than zero.
3. Zero gradients: A line with a zero gradient is a horizontal line. For a line that has a slope of zero, the value of the gradient is zero.
4. Undefined gradients: A line with an undefined gradient is a vertical line.
The gradient of a line is calculated by dividing the difference between the y- and x-coordinates.
The formula for the gradient of a line can be written as:
Gradient of a line =
where (x₁ ,y₁) and (x₂ ,y₂) are any two points on the line.
The gradient of the given straight line on a graph can be determined as follows:
Step 1: Take any two points on the given line and write their coordinates.
Step 2: Consider the first point’s coordinates as (x₁, y₁) and the second point’s coordinates as (x₂, y₂).
Step 3: Find the change in the y-axis: (y₂-y₁)
Step 4: Find the change in the x-axis: (x₂-x₁)
Step 5: Substitute the change in y and x-axis in the gradient formula.
Step 6: Simplify it if required to get the value of the gradient of a given straight line.
Let's look at some examples.
Example 1 : Calculate the gradient of the line drawn below.
Example 2 : Calculate the gradient of the line drawn below .
The gradient of the straight line that passes through the given points can be determined as follows:
Step 1: Consider the first point’s coordinates as (x₁, y₁) and the second point’s coordinates as (x₂, y₂)
Step 2: Find the change in the y-axis: (y₂-y₁)
Step 3: Find the change in the x-axis: (x₂-x₁)
Step 4: Substitute change in y and x-axis in the gradient formula.
Step 5: Simplify it to get the value of the gradient of the straight line.
Let's look at an example.
Example 1 : Find the gradient of the line that passes through (-5, 2) and (3, 4).
The main topics in GCSE Maths are:
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Although many people think of GCSE maths as a difficult subject, with the correct training and preparation,you can master it in time. You can practice GCSE Maths topic-wise questions daily to improve speed, accuracy, and time and to score high marks in the GCSE Maths exam.
A grade of 4 or 5 would be considered "good" because the government has established a 4 as the passing grade; a grade of 5 is seen as a strong pass. Therefore, anything that exceeds this level would be considered good. You can practice GCSE Maths topic-wise questions to score good grades in the GCSE Maths exam.
You can get a high score in GCSE Maths through meticulous practice of GCSE Maths topic-wise questions and GCSE Maths past papers.
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