10. Which equation represents the graphed line?
Answer: D
y = 1/3x + 1
The equation that represents the graphed line is y = 1/3x + 1, indicating a positive slope and a y-intercept of 1.
A) y = -1/3x + 3
This option represents a line with a negative slope of -1/3, which means it would decrease as x increases. Additionally, its y-intercept of 3 is not consistent with the given line that intersects the y-axis at 1.
B) y = 3x - 7
This equation has a steep positive slope of 3 and a y-intercept of -7. This suggests a much steeper increase than the line in question, which does not match the characteristics of the graphed line.
C) y = 3x + 7
With a slope of 3 and a y-intercept of 7, this option indicates a line that rises sharply and intersects the y-axis much higher than the line represented by the correct answer. This makes it inconsistent with the graphed line.
D) y = 1/3x + 1
This is the correct option as it correctly describes a line with a slope of 1/3 and a y-intercept of 1. The positive slope indicates that the line rises gradually, consistent with the graph's appearance.
Conclusion
The choice of y = 1/3x + 1 is confirmed as the correct equation for the graphed line due to its accurate slope and y-intercept. All other options fail to match the slope or intercept of the graphed line, clearly demonstrating their inaccuracy.