How to find the gradient of a line?
Understand the Problem
The question is asking for the method to calculate the gradient (or slope) of a line. The gradient is typically found by using the formula (change in y) / (change in x) between two points on the line.
Answer
The gradient (slope) of the line is given by: $$ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} $$
Answer for screen readers
The gradient (slope) of the line is calculated using the formula:
$$ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} $$
Steps to Solve
- Identify the points
First, identify the two points on the line you want to use. Let's denote them as $(x_1, y_1)$ and $(x_2, y_2)$.
- Calculate the change in y
Next, calculate the change in the y-coordinates of the two points. This can be done using the formula:
$$ \Delta y = y_2 - y_1 $$
- Calculate the change in x
Then, calculate the change in the x-coordinates of the two points with the formula:
$$ \Delta x = x_2 - x_1 $$
- Compute the gradient
Now, compute the gradient (slope) using the values obtained from steps 2 and 3 with the formula:
$$ \text{slope} = \frac{\Delta y}{\Delta x} $$
- Substituting values
Substitute the values of $\Delta y$ and $\Delta x$ into the slope formula to find the gradient:
$$ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} $$
The gradient (slope) of the line is calculated using the formula:
$$ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} $$
More Information
The gradient of a line represents how steep the line is and in which direction it is going. A positive gradient means the line rises from left to right, while a negative gradient means it falls. A slope of zero indicates a horizontal line, and an undefined slope indicates a vertical line.
Tips
- Forgetting to correctly identify the points: Always ensure that the values for $(x_1, y_1)$ and $(x_2, y_2)$ are chosen accurately.
- Mixing up the order of subtraction: Remember that the order matters; it is $(y_2 - y_1)$ and $(x_2 - x_1)$.
- Not simplifying the fraction if possible: If $\Delta y$ and $\Delta x$ have common factors, simplify to get the most reduced form.
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