the graph shows the distance traveled by two cars over several minutes. drag and drop the appropriate symbol…

Explanation:

Step1: Recall the formula for rate (speed)

The rate (speed) is calculated as ( \text{rate}=\frac{\text{distance}}{\text{time}} ). In a distance - time graph, the slope of the line represents the rate. The formula for the slope ( m ) of a line passing through two points ((x_1,y_1)) and ((x_2,y_2)) is ( m=\frac{y_2 - y_1}{x_2 - x_1} ). For a line passing through the origin ((0,0)) and another point ((x,y)), the slope ( m=\frac{y}{x} ).

Step2: Compare the slopes of the two lines

Let's assume two points on the line of Car A: say ((x_{A1},y_{A1})=(0,0)) and ((x_{A2},y_{A2})), and for Car B: ((x_{B1},y_{B1})=(0,0)) and ((x_{B2},y_{B2})). If we take (x) - values (time) to be the same for both cars (for a fair comparison), we can see that for a given (x) (time), (y_{B}>y_{A}) (distance of Car B is greater than that of Car A). Using the slope formula (m=\frac{y}{x}) (since (x_1 = y_1=0)), if (x) is the same (non - zero) and (y_{B}>y_{A}), then (\frac{y_{B}}{x}>\frac{y_{A}}{x}). The slope of the line for Car B is steeper than the slope of the line for Car A.

Answer:

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