Find the gradient of the line joining (-2, 4) and (3, 3)

The gradient (or slope) of a line joining two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

For the points \((-2, 4)\) and \((3, 3)\):

- \(x_1 = -2\), \(y_1 = 4\)
- \(x_2 = 3\), \(y_2 = 3\)

Substituting these values into the formula:

\[ m = \frac{3 - 4}{3 - (-2)} \]

\[ m = \frac{-1}{3 + 2} \]

\[ m = \frac{-1}{5} \]

Thus, the gradient of the line joining the points \((-2, 4)\) and \((3, 3)\) is \(\frac{-1}{5}\).

If you have any questions or want more details, let me know!

Here are some related questions for further exploration:

1. How do you find the equation of a line given two points?
2. What is the physical interpretation of a line’s gradient?
3. How can the gradient be used to determine if two lines are parallel?
4. What is the difference between the gradient of a line and the gradient of a curve?
5. How do you find the y-intercept of a line using its gradient and a point on the line?
6. How do you determine if a point lies on a given line?
7. What are the effects of changing the gradient on the steepness of a line?
8. How can the concept of gradient be applied in fields like physics or economics?

**Tip**: To check if a point lies on a line, substitute the point's coordinates into the line's equation and verify if the equation holds true.

Learn how to find the gradient (slope) of a line connecting the points (-2, 4) and (3, 3) using the slope formula. Detailed step-by-step solution provided. Suitable for Grades 7-9 students.

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