Which of the following could be an equation of the line graphed in the xy-plane above?
y = x + 3 could be an equation of the line graphed in the xy-plane above.
This equation represents a line with a positive slope of 1 and a y-intercept of 3, indicating that the line rises as it moves from left to right and crosses the y-axis at the point (0, 3), which corresponds to the graph shown.
This equation has a negative slope of -1 and a y-intercept of -3. Thus, the line would slope downwards from left to right, crossing the y-axis at (0, -3). This does not match the characteristics of the graph provided, which shows an upward slope.
Similar to option A, this equation has a negative slope of -1, but it crosses the y-axis at (0, 3). While it has the same y-intercept as the correct answer, its slope indicates that the line slopes downward from left to right, which contradicts the upward trend of the graph.
This equation features a positive slope of 1, indicating the line rises as it moves to the right. However, it has a y-intercept of -3, which means it crosses the y-axis at (0, -3). This point does not align with the graph, which shows the line crossing at (0, 3).
This equation has a positive slope of 1 and a y-intercept of 3, meaning it rises from left to right and intersects the y-axis at (0, 3). This matches the behavior of the line depicted in the graph, confirming that it is the accurate representation.
The equation y = x + 3 accurately describes the line shown in the graph due to its positive slope and correct y-intercept. The other choices either have negative slopes or incorrect y-intercepts, making them incompatible with the graph's characteristics. Thus, understanding the relationship between slope and intercepts is crucial for identifying the correct linear equation.
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