To find the equation of the line shown on the graph, we use the formula for the equation of a straight line:

$y = mx + c$

Where:

• $m$ is the slope (gradient) of the line.
• $c$ is the y-intercept (where the line crosses the y-axis).

Step 1: Determine the Gradient ($m$)

To find the gradient ($m$), we use two points on the line. Based on the graph:

• One point is $(0, 1)$ (where the line crosses the y-axis).
• Another point could be $(2, 3)$.

The gradient $m$ is calculated as follows:

$m = \frac{{\text{change in y}}}{{\text{change in x}}} = \frac{3 - 1}{2 - 0} = \frac{2}{2} = 1$

So, $m = 1$.

Step 2: Find the Y-Intercept ($c$)

From the graph, it is clear that the line crosses the y-axis at $y = 1$. Thus, $c = 1$.

Step 3: Write the Equation

Substituting $m = 1$ and $c = 1$ into the equation:

$y = 1x + 1 \quad \text{or simply} \quad y = x + 1$

Final Answer

The equation of the line is: $\boxed{y = x + 1}$

Would you like further details or have any questions about the solution?

Related Questions:

1. How do you find the gradient if the points are not on the axis?
2. What happens to the equation if the gradient is negative?
3. How can you identify a parallel line from the equation?
4. What is the equation of a line that is perpendicular to $y = x + 1$?
5. How do you find the equation if the line does not intercept the y-axis directly?

Tip:

Always ensure you correctly identify two clear points on the graph when finding the gradient to avoid calculation errors.