Let's analyze the graph to answer both parts of the question:

a) What is the $y$-intercept of this line?

The $y$-intercept is where the line crosses the $y$-axis. From the graph, we can observe that the line crosses the $y$-axis at $y = 5$. So, the $y$-intercept is:

$y = 5$

b) What is the gradient (slope) of this line?

The gradient (slope) of a line is calculated by the formula:

$\text{slope} = \frac{\Delta y}{\Delta x} = \frac{\text{change in } y}{\text{change in } x}$

From the graph, we can select two points on the line to calculate the slope. Let’s use the points:

• $(0, 5)$ (the $y$-intercept)
• $(-5, 0)$ (where the line crosses the $x$-axis)

The change in $y$ is from 5 to 0, so $\Delta y = 5 - 0 = 5$.

The change in $x$ is from 0 to -5, so $\Delta x = 0 - (-5) = 5$.

Thus, the gradient is:

$\text{slope} = \frac{5}{5} = 1$

Final Answers:

• $y$-intercept: $y = 5$
• Gradient: $1$

Do you want more details or have any questions?

Here are some related questions:

1. What is the general form of a linear equation?
2. How can you calculate the slope if the points are not given clearly?
3. What happens if the gradient of a line is negative?
4. How does the slope affect the angle of the line with respect to the $x$-axis?
5. How can we verify the $y$-intercept using the equation of the line?

Tip: The gradient tells you how steep a line is. A larger gradient means a steeper line!