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.