Question 9

y = 1/2x + 2

The equation of the line graphed in the xy-plane is y = 1/2x + 2, indicating that the line has a slope of 1/2 and a y-intercept of 2.

A) y = x + 2

This option suggests a slope of 1, which is steeper than the line represented in the graph. The y-intercept is correctly identified as 2, but the slope does not match the line's actual slope, making this choice incorrect.

B) y = 1/2x + 2

This option accurately represents the line with a slope of 1/2 and a y-intercept of 2. The line rises slowly, consistent with the graph's depiction, confirming that this is the correct equation.

C) y = 3/2x + 2

This option indicates a slope of 3/2, which is steeper than the slope of the line shown in the graph. Although the y-intercept is correct, the incorrect slope disqualifies this option from being the correct answer.

D) y = 2x + 4

This option has a slope of 2, indicating a much steeper line than what is represented in the graph. Furthermore, the y-intercept of 4 is also incorrect, as the graph shows a y-intercept of 2, making this option invalid.

Conclusion

The correct equation of the line is y = 1/2x + 2, as it accurately reflects both the slope and the y-intercept shown in the graph. All other options either have incorrect slopes or y-intercepts, leading to their disqualification as potential correct answers.