Final answer:
The value of the slope remains unchanged after dilation because both the rise and the run are multiplied by the same scale factor. In a proportion-related example, a scale factor of 1:2 and a scale dimension of 4 would correspond to an actual dimension of 8, demonstrating that scale transformations preserve ratios.
Step-by-step explanation:
The slope of a line after dilation remains the same as the slope before dilation. So, if you have a line with a slope of 4 and it undergoes a dilation with a scale factor, the slope of the line will still be 4 after the dilation. This is because both the rise and run between any two points on the line are multiplied by the same scale factor during the dilation, preserving the ratio which defines the slope.
To understand this with a proportion, let's consider the sample problem with scale dimensions. If the scale factor is 1:2 and the scale dimension is given as 4 (the 'run'), we can set up a proportion to find the actual dimension (the 'rise'):
1:2 = 4:x
To solve for 'x', we cross-multiply to get:
1*x = 4*2
x = 8
Therefore, the actual 'rise' corresponding to a 'scale run' of 4 at a scale factor of 1:2 is 8. Similarly, when applying a scale factor to a line's slope, the 'rise' and 'run' in the slope ratio are both multiplied by the same scale factor, so the slope itself does not change.