Question

Point P does not lie on the line with the equation y =-2x+6. A dilation of this line is performed with center P and a scale factor not equal to 1. Which equation could represent the resulting line?

Answer 1

The equation of a line resulting from a dilation with center point P not lying on the original line with equation y = -2x + 6 will be parallel to the original line, having the same slope of -2 but a different y-intercept, represented as y = -2x + b.

Step-by-step explanation:

When a dilation of a line is performed with a center point P that does not lie on the line, and with a scale factor not equal to 1, the resulting line will be parallel to the original line. Therefore, the slope of the resulting line will be the same as the original, which is -2 in the given equation y = -2x + 6. Since the scale factor is not equal to 1, and the dilation is centered at point P not on the original line, the y-intercept will be different. A possible resulting line could have an equation like y = -2x + b, where b is the new y-intercept that depends on the location of point P and the scale factor.