Let's work through the problem. The task is to write the equation of the line shown in the image in slope-intercept form, which is:

$y = mx + b$

Where:

• $m$ is the slope of the line,
• $b$ is the y-intercept.

From the graph:

1. Find the slope (m):

   • The slope is calculated by the formula $m = \frac{{\text{change in y}}}{{\text{change in x}}}$.
   • We can pick two points on the line. From the graph, it appears the line passes through points (1, 6) and (4, 0).
   • Calculate the slope:

   $m = \frac{{0 - 6}}{{4 - 1}} = \frac{{-6}}{{3}} = -2$

2. Find the y-intercept (b):

   • The y-intercept is the value of $y$ where the line crosses the y-axis, which appears to be $b = 6$ from the graph.

Thus, the equation in slope-intercept form is:

$y = -2x + 6$

Let me know if you need further clarifications or additional steps!

Here are some related questions to help deepen your understanding:

1. How do you find the slope of a line if you are given two points?
2. What is the relationship between slope and the direction of the line?
3. How can you write the equation of a line if you're given the slope and y-intercept directly?
4. What does it mean when a line has a positive slope versus a negative slope?
5. How do you graph a line once you have its equation in slope-intercept form?

Tip: When finding the slope from two points, always pick points where the coordinates are easy to read and avoid points that are too close together to reduce potential calculation errors.