To determine the equation of the line in slope-intercept form $y = mx + b$ from the given graph, we need to find the slope $m$ and the y-intercept $b$.

Step-by-Step Solution:

1. Identify two points on the line:

   • From the graph, two points on the line are $(-8, -6)$ and $(8, 6)$.

2. Calculate the slope $m$:

   • The slope $m$ is calculated as the change in y divided by the change in x: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(x_1, y_1) = (-8, -6)$ and $(x_2, y_2) = (8, 6)$: $m = \frac{6 - (-6)}{8 - (-8)} = \frac{6 + 6}{8 + 8} = \frac{12}{16} = \frac{3}{4}$

3. Determine the y-intercept $b$:

   • The y-intercept $b$ is where the line crosses the y-axis. From the graph, it's clear that the line crosses the y-axis at $y = 0$.

4. Write the equation in slope-intercept form:

   • With $m = \frac{3}{4}$ and $b = 0$, the equation of the line is: $y = \frac{3}{4}x$

Therefore, the equation of the line in slope-intercept form is: $y = \frac{3}{4}x$

Would you like further details or have any questions?

Related Questions:

1. How do you find the equation of a line given two points?
2. What is the significance of the slope in the equation of a line?
3. How can you determine the y-intercept from a graph?
4. What are the different forms of a linear equation and how do you convert between them?
5. How does changing the slope and y-intercept affect the graph of a line?

Tip:

Always verify the points you choose for calculating the slope to ensure accuracy in determining the equation of the line.