10. Which of the following could be an equation of the line graphed in the xy-plane above?
Answer: D
y = x + 3
The equation of the line that is graphed in the xy-plane is y = x + 3, indicating a positive slope and a y-intercept of 3.
A) y = -x - 3
This option represents a line with a negative slope and a y-intercept of -3, which does not match the characteristics of the line in the graph. The line would decline from left to right, contrasting with the upward slope observed.
B) y = -x + 3
Similar to option A, this option features a negative slope and a y-intercept of 3. While it intersects the y-axis at the correct point, its slope suggests the line descends from left to right, which is not consistent with the line shown in the graph.
C) y = x - 3
This equation has a positive slope but a y-intercept of -3. The line would rise from left to right but would cross the y-axis below the origin, which does not align with the graph that intersects the y-axis at +3.
D) y = x + 3
This is the correct equation representing the line in the graph. It has a positive slope of 1 and a y-intercept of 3, matching the upward trend and intersection point of the line depicted.
Conclusion
The correct answer, y = x + 3, accurately reflects the characteristics of the graphed line in the xy-plane. All other options fail to match both the slope and the y-intercept of the line, confirming that D is the only viable choice.