Question

how can jordan use the plot to check the reasonableness of his answer?
his slope should be positive because the coordinates of all the plotted points are positive.
his slope should be positive because the trend line is slanted up to the right.
his slope should be negative because there are plotted points not on the line.
his slope should be negative because the x - coordinate of each plotted point is less than the y - coordinate.

Explanation:

Step1: Recall the property of slope

The slope of a line is positive if the line rises from left - to - right and negative if it falls from left - to - right.

Step2: Analyze each option

• Option 1: Just because the coordinates of points are positive does not determine the sign of the slope. For example, a line \(y=-x + 5\) has positive \(x\) and \(y\) values in the first quadrant but a negative slope.
• Option 2: The trend line is slanted up to the right. By the definition of slope ( \(m=\frac{\Delta y}{\Delta x}\), when \(x\) increases, \(y\) increases), the slope is positive.
• Option 3: The presence of points not on the line does not affect the sign of the slope of the trend line.
• Option 4: Comparing \(x\) and \(y\) coordinates of points does not determine the sign of the slope. For example, for the point \((1,2)\) and \((2,1)\) in a non - trend - line context, the relationship between \(x\) and \(y\) values does not give the slope sign.

Answer:

His slope should be positive because the trend line is slanted up to the right.