To determine the equation of the line in slope-intercept form (which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept), we will follow these steps:

Step 1: Identify the slope ($m$)

The slope is the rise over the run, or the change in $y$ divided by the change in $x$. From the graph:

• The line passes through the points $(-6, -4)$ and $(6, 6)$.

Using the formula for the slope: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (-4)}{6 - (-6)} = \frac{6 + 4}{6 + 6} = \frac{10}{12} = \frac{5}{6}$

So, the slope $m = \frac{5}{6}$.

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

The y-intercept is the value of $y$ when $x = 0$. By inspecting the graph, we can see that the line crosses the y-axis at $(0, 1)$. Therefore, the y-intercept $b = 1$.

Final Equation

Substituting $m = \frac{5}{6}$ and $b = 1$ into the slope-intercept form equation: $y = \frac{5}{6}x + 1$

Thus, the equation of the line is: $y = \frac{5}{6}x + 1$

Would you like more details or have any other questions?

Here are 5 related questions to explore:

1. How can we convert this slope-intercept form into standard form?
2. What is the significance of the slope and y-intercept in real-world scenarios?
3. How would the equation change if the slope were negative?
4. What is the equation of a line parallel to this one?
5. How would you find the equation of a perpendicular line to this one?

Tip: Always verify points on the graph by substituting them into your final equation.