Final answer:
The y-intercept of the equation y = 9 + 3x is found by substituting 0 for x, which results in y = 9. The y-intercept is the point (0, 9), and it represents where the line crosses the y-axis. The slope of the line is 3, indicating a rise of 3 units in y for every unit increase in x.
Step-by-step explanation:
To find the y-intercept of a line given by an equation, we substitute 0 for the variable x and solve for y. The given equation seems to have a typo; however, based on the additional information provided, the correct equation should be y = 9 + 3x. Substituting 0 for x gives us y = 9 + (3 × 0), which simplifies to y = 9. Therefore, the y-intercept is the point (0, 9), meaning the line intersects the y-axis at 9 units above the origin.
Understanding the slope, which is the change in y divided by the change in x, offers additional insights into the equation of a line. In our case, the slope is 3, indicating that for every 1 unit increase in x, y increases by 3 units. This consistent rate of change confirms the linear nature of the graph.
The concept of the y-intercept is crucial when graphing a line and interpreting the relationship it represents. In some contexts, interpreting the y-intercept may not be practical or necessary, such as when it is impossible for the x variable to be zero in a real-world scenario. However, it remains a vital part of understanding the algebra of straight lines.