Final answer:In Mathematics, to match a given linear regression equation −0.677x + 52.3 with a graph, we search for a downward-sloping line that crosses the y-axis at 52.3.Explanation:The subject of the student's question is Mathematics, focused on the concept of the regression equation and its graphical representation. The question appears to be at a High School level, specifically concerning a linear regression equation that needs to be matched with its appropriate graph. The regression equation given is −0.677x + 52.3, which indicates a linear relationship between the variables x and y.To match this equation with a graph, we must consider its components. The slope of the line is −0.677, which tells us that for each one-unit increase in x, the value of y decreases by 0.677. The y-intercept is 52.3, meaning the graph of the equation will cross the y-axis at the point (0, 52.3).Looking for a graph, we would be searching for a line that slopes downwards from left to right (a negative slope), and crosses the y-axis slightly above the 50 mark. This systematic approach to verifying the slope and the y-intercept on a given graph will enable the student to correctly match the regression equation with the visual representation....

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