Which of the following is an equation of the line graphed in the xy -plane above?
y = 1/2x + 2 is the equation of the line graphed in the xy-plane.
The line depicted in the graph has a slope of 1/2 and a y-intercept of 2, which corresponds directly to the equation y = 1/2x + 2. This means that for every increase of 1 unit in x, y increases by 0.5 units, matching the line's visual representation.
This equation has a slope of 1, indicating that for every 1 unit increase in x, y increases by 1 unit. This is steeper than the line in the graph, which clearly shows a gentler slope, making this option incorrect.
This equation accurately reflects the line's slope of 1/2 and y-intercept of 2. The graph shows that the line crosses the y-axis at 2 and rises by 0.5 units for each 1 unit increase in x, confirming this choice as correct.
With a slope of 3/2, this equation suggests that for every 1 unit increase in x, y would increase by 1.5 units. This is much steeper than the line shown in the graph, which does not match the slope of the depicted line.
This equation features a slope of 2, which indicates a steep incline, meaning y increases by 2 units for every 1 unit increase in x. The graph illustrates a much less steep line, thus making this option incorrect.
Analyzing the slope and y-intercept of the line in the graph allows us to determine that the correct equation is y = 1/2x + 2. This equation accurately represents the graphical relationship of x and y values, while the other choices present slopes that do not align with the visual representation of the line.
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