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

Step 1: Find the Slope ($m$)

The slope $m$ is calculated as: $m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

From the graph, identify two points on the line:

• Point 1: $(-6, 3)$
• Point 2: $(6, 9)$

Now substitute into the slope formula: $m = \frac{9 - 3}{6 - (-6)} = \frac{6}{12} = \frac{1}{2}$

The slope $m$ is $\frac{1}{2}$.

Step 2: Find the Y-Intercept ($b$)

The y-intercept $b$ is the point where the line crosses the $y$-axis. From the graph, the line crosses the $y$-axis at $(0, 6)$.

Thus, $b = 6$.

Step 3: Write the Equation

Substitute the slope $m = \frac{1}{2}$ and y-intercept $b = 6$ into the slope-intercept form $y = mx + b$: $y = \frac{1}{2}x + 6$

Final Answer:

The equation of the line in slope-intercept form is: $y = \frac{1}{2}x + 6$

Do you want me to explain how to verify the slope or graph the equation? Let me know if you have more questions!

Related Questions:

1. How can you calculate the slope if only the graph is provided?
2. What is the general form of a linear equation, and how does it relate to slope-intercept form?
3. How do you determine the slope if the line passes through vertical or horizontal axes?
4. Can you graph a line given its equation in slope-intercept form?
5. How does changing the slope $m$ affect the steepness of the line?

Tip:

Always choose two clear points from a graph to calculate the slope accurately!