Final answer:
The scale factor of the dilation from the line 7y = 2x + 7 to the line -2x + 7y = 28 is 4. This is determined by comparing the coefficients and constants in both equations.
Step-by-step explanation:
When a line is dilated by a scale factor centered at the origin, the coefficients of the variables in the equation of the line are scaled by this factor. The original line in your question is 7y = 2x + 7, and the image of the line after dilation is given by -2x + 7y = 28.
To find the scale factor of the dilation, we can compare the coefficients of corresponding variables.
First, we need to isolate 'y' in both equations to make it easy to compare:
- Original line: y = (2/7)x + 1
- Dilated line: y = (4/7)x + 4
Now, let's look at the coefficients of 'x'. In the original line it is 2/7 and in the dilated line it is 4/7.
To go from 2/7 to 4/7, you would multiply by 2.
However, when we look at the constants, we see that the constant in the original equation is 1, and in the dilated equation, it is 4, which means the constant was multiplied by 4 to get the dilated equation.
Therefore, this indicates that the dilation scale factor for the coefficient and constant is 4.
Overall, this means that each value is multiplied by 4, and therefore the scale factor is 4.