To determine the equation of the straight line shown in the image, we need to find the slope ($m$) and the $y$-intercept ($c$) of the line. The equation should be in the form $y = mx + c$.

Step 1: Identify two points on the line

From the graph, we can observe that the line passes through the points:

• $(-6, 0)$ (when $x = -6$, $y = 0$)
• $(0, 6)$ (when $x = 0$, $y = 6$)

Step 2: Find the slope $m$

The slope of the line $m$ is calculated using the formula:

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

Substituting the coordinates of the two points:

$m = \frac{6 - 0}{0 - (-6)} = \frac{6}{6} = 1$

So, the slope $m = 1$.

Step 3: Find the $y$-intercept $c$

The $y$-intercept is the point where the line crosses the $y$-axis. From the graph, we can clearly see that the line crosses the $y$-axis at $y = 6$. Therefore, $c = 6$.

Step 4: Write the equation

Now that we know $m = 1$ and $c = 6$, the equation of the line is:

$y = x + 6$

This is the equation of the straight line.

Would you like any further details or have any questions?

Here are 5 related questions:

1. How do you calculate the slope if the two points are fractions?
2. What is the significance of the $y$-intercept in the equation of a line?
3. How would the equation change if the slope was negative?
4. How do you find the equation if only the slope is given, but no points are provided?
5. How can you determine if two lines are parallel or perpendicular using their slopes?

Tip: When calculating the slope, ensure that you subtract the coordinates in the same order to avoid sign errors.