Question

the line y=2x-4 is dilated bt a scale factor of 3/2 and centered at the origin. Write an equation that represent that image of the line after dilation

Answer 1

Answer:  $y = 2x -6$

Step-by-step explanation:

Since, If (x,y) represents the coordinates of a line, then after dilation about the origin by the scale factor k, the coordinates of the resultant line will get by the rule,

$(x,y)\rightarrow (kx,ky)$

Here, The equation of the given line is,

y = 2x - 4

x-intercept and y-intercept of the line are (2,0) and (0,-4) respectively,

Hence, the line y = 2x - 4 will be passes through the points (2,0) and (0,-4),

By the above property,

The dilated line about the origin will be passes through the points (3,0) and (0,-6),   ( Because (3/2× 2, 3/2×0) = (3,0) and (3/2×0, 3/2×-4) = (0,-6) )

Hence, the equation of transformed line after dilation,

$y-0 = \frac{-6-0}{0-3}(x-3)$    

$y-0=2(x-3)$

$y-0=2x-6$

$y=2x-6$

Answer 2

To solve this problem you must apply the proccedure shown below:

 1. You have the the line y=2x-4 is dilated by a scale factor of 3/2 and centered at the origin.

 2. The form of the a line is y=mx+b, where m is the slope and b is the y-intercept. As dilation conserves the parallelism, the dilated linw will have the same slolpe: 2

 m=2

 3. By using the y-intercept, you have:

 (0,-4)

 0x3/2=0
 -4(3/2)=-6

 (0,-6)

 4. Therefore, the equation that represent that image of the line after dilation is:

 m=2
 b=-6

 y=2x-6