To find the equation of the line shown in the graph, we use the slope-intercept form of a line:

$y = mx + b$

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

Step 1: Determine the slope ($m$)

The slope is the change in $y$ divided by the change in $x$, which can be found using two points on the line.

From the graph, we can see the line passes through:

• Point 1: $(0, -6)$
• Point 2: $(3, -3)$

The formula for the slope is:

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

Substitute the points $(x_1, y_1) = (0, -6)$ and $(x_2, y_2) = (3, -3)$:

$m = \frac{-3 - (-6)}{3 - 0} = \frac{-3 + 6}{3} = \frac{3}{3} = 1$

Step 2: Determine the y-intercept ($b$)

From the graph, we can see that the line crosses the y-axis at $(0, -6)$. Thus, the y-intercept $b = -6$.

Final Equation

Now, using the slope $m = 1$ and y-intercept $b = -6$, the equation of the line is:

$y = x - 6$

Would you like further details on the steps? Here are five related questions for deeper exploration:

1. How do you find the slope of a line if only one point is visible?
2. What happens to the equation if the slope is negative?
3. How do you solve for the y-intercept if it is not clearly visible on the graph?
4. What is the difference between the slope-intercept form and point-slope form of a line?
5. Can a line have a slope of zero, and what would its equation look like?

Tip: When finding the slope, make sure you carefully pick points where the line crosses grid intersections to avoid calculation errors.