To find the equation of the straight line shown in the graph, we need to express it in the form $y = mx + c$, where:

• $m$ is the slope (or gradient) of the line.
• $c$ is the y-intercept (the value of $y$ when $x = 0$).

Step 1: Identify the y-intercept

From the graph, the line crosses the y-axis at $y = 4$. So, $c = 4$.

Step 2: Find the slope ($m$)

The slope $m$ is calculated using two points on the line. Let's pick two points:

• $(0, 4)$ (where the line crosses the y-axis).
• $(2, 0)$ (another point where the line crosses the x-axis).

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the values: $m = \frac{0 - 4}{2 - 0} = \frac{-4}{2} = -2$

Step 3: Write the equation

Now that we have both $m = -2$ and $c = 4$, the equation of the line is: $y = -2x + 4$

Would you like any further details or clarifications?

Here are 5 related questions you could explore:

1. How would the equation change if the slope were positive?
2. Can the equation be written in a different form, such as point-slope form?
3. What is the significance of the y-intercept in real-world applications?
4. How would the graph look if the y-intercept was negative?
5. How do you find the slope when the line is horizontal?

Tip: When calculating the slope, always use two distinct points on the line for the most accurate result.