Which equation represents the graphed line?
y = 1/3x + 1 represents the graphed line.
This equation accurately reflects the slope and y-intercept observed in the graph. The slope of 1/3 indicates a gentle rise, while the y-intercept at 1 confirms the line's starting point on the y-axis.
This equation features a negative slope of -1/3, indicating a downward trend, which contradicts the upward slant of the graphed line. Additionally, the y-intercept at 3 suggests that it intersects the y-axis much higher than the line shown in the graph.
With a slope of 3, this equation represents a much steeper incline than that of the graphed line. The y-intercept at -7 is also significantly lower than the observed intersection point on the y-axis, making this option inconsistent with the graphed line.
Similar to option B, this equation has a steep slope of 3, which does not match the gradual incline of the graphed line. The y-intercept of 7 is also higher than what is shown in the graph, further disqualifying this choice as a representation of the line.
This equation accurately captures both the slope and the y-intercept of the graphed line. The slope of 1/3 aligns with the gentle upward trend of the line, and the y-intercept of 1 correctly indicates where the line intersects the y-axis.
The equation y = 1/3x + 1 correctly represents the graphed line due to its matching slope and y-intercept. Other choices fail to align with the essential characteristics of the line, either through incorrect slopes or inappropriate intercepts, reinforcing that choice D is the only viable option. Understanding the relationship between slope and intercept is crucial in accurately interpreting linear equations and their graphical representations.
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