Hey, I asked this question before, but never received a response.
The line represented by 2y = 6x + 8 is dilated by a scale factor of k centered at the origin, such that the image of the line has an equation of y = 3x+ 12. What is the scale factor?
As I said before, the new line is twice as far away from (0,0), so the dilation must be 2
oops. Make that 3
To find the scale factor, we need to compare the corresponding coefficients of the original line and the dilated line. In the original line, we have the equation 2y = 6x + 8.
First, let's rewrite the original equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To do this, we divide both sides of the equation by 2:
2y/2 = (6x + 8)/2
y = 3x + 4
From the dilated line given in the question, we can see that the slope is 3. The scale factor, denoted as k, represents the ratio of the coefficients of the slopes of the original line to the dilated line.
In this case, the slope of the original line is 3, and the slope of the dilated line is also 3. Therefore, the scale factor k is equal to 1, since the ratio of the two slopes is 3/3 = 1.
Hence, the scale factor in this scenario is 1.