To find the gradient (or slope) of the line segment in the graph, we use the formula for the gradient between two points $A(x_1, y_1)$ and $B(x_2, y_2)$, which is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

From the graph:

• Point $A$ has coordinates $(-1.5, 2.5)$
• Point $B$ has coordinates $(0, 1.5)$

Now we can plug the values into the formula:

$m = \frac{1.5 - 2.5}{0 - (-1.5)} = \frac{-1}{1.5}$

Simplifying the fraction:

$m = \frac{-2}{3}$

So, the gradient of the line segment is $m = -\frac{2}{3}$.

Would you like more details on this or have any other questions?

Here are five related questions to expand your understanding:

1. How do you calculate the gradient between two points without a graph?
2. What does a negative gradient indicate about the direction of a line?
3. How would the gradient change if point $B$ were shifted vertically?
4. What is the difference between the gradient and the y-intercept?
5. How does the steepness of a line relate to the magnitude of the gradient?

Tip: The gradient gives the rate of change of the line. A larger magnitude means a steeper slope, while a smaller magnitude means a flatter line.