To write the equation of the line shown in the image, we need to determine its slope and y-intercept.

1. Identify two points on the line: From the graph, we can see two points that the line passes through:

   • Point 1: $(2, -1)$
   • Point 2: $(6, 3)$

2. Calculate the slope ($m$): The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the values from the points: $m = \frac{3 - (-1)}{6 - 2} = \frac{4}{4} = 1$

3. Find the y-intercept ($b$): The y-intercept is the value of $y$ when $x = 0$. We can use the slope-intercept form of the equation $y = mx + b$. Using one of the points $(2, -1)$: $-1 = 1(2) + b \implies -1 = 2 + b \implies b = -3$

4. Write the equation: The equation of the line in slope-intercept form $y = mx + b$ is: $y = x - 3$

This is the equation of the line shown in the image.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would the equation change if the slope was steeper?
2. What is the general form of a line equation and how does it relate to the slope-intercept form?
3. Can you find the equation of a line parallel to the given line?
4. How would you find the equation of a line perpendicular to the given line?
5. What happens to the y-intercept if you shift the line up or down?

Tip: Always start by identifying key points on a graph to help find the slope and y-intercept when writing the equation of a line.