To determine the equation of the straight line in the form $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept, let's proceed with the following steps:

1. Identify two points on the line

From the graph, we can choose two clear points that lie on the line:

• The line crosses the y-axis at the point $(0, 6)$. This means the y-intercept $c = 6$.
• Another point on the line is $(2, 0)$ because the line crosses the x-axis there.

2. Calculate the slope $m$

The slope $m$ of a line is calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(0, 6)$ and $(2, 0)$: $m = \frac{0 - 6}{2 - 0} = \frac{-6}{2} = -3$ Thus, the slope of the line is $m = -3$.

3. Write the equation of the line

Now that we know the slope $m = -3$ and the y-intercept $c = 6$, the equation of the line is: $y = -3x + 6$

This is the equation of the line in the required form.

Would you like more details or further clarifications?

Related questions:

1. How can you derive the equation of a line from just the slope and one point?
2. What is the significance of the y-intercept in the equation of a line?
3. How do you calculate the slope if only one point and the equation are given?
4. Can you describe a method to find the equation if the line doesn't cross the axes clearly?
5. How does changing the slope affect the appearance of the line?

Tip:

Always check two distinct points on the graph to accurately calculate the slope when determining the equation of a line.