Line p passes through the points (–2,7) and (6,3). What is the slope of the image of p after a dilation with a scale factor of 2 centered at (–3,1)?

The slope of a line remains unchanged under dilation. Dilation changes the position of the points on the line, but it does not change the direction of the line. Therefore, the slope of the image of line p after a dilation with a scale factor of 2 centered at (-3,1) is the same as the original slope of line p.

To find the slope of line p, we can use the formula for the slope of a line given two points, (x1, y1) and (x2, y2), which is (y2 - y1) / (x2 - x1).

Substituting the given points into the formula, we get:

Slope of line p = (3 - 7) / (6 - (-2)) = -4 / 8 = -0.5

So, the slope of the image of line p after the dilation is also -0.5.