Question

The equation 5x−4y=24 is dilated by a scale factor of 0.2 centered at the origin. What is the equation of the image of the line?A)y=1.5x−6.0B)y=1.25x−4.8C)y=0.25x−6.0D)y=1.25x-1.2

Answer 1

we are given the following line equation:

$5x-4y=24$

First, we will solve for "y", first by subtracting "5x" on both sides:

$-4y=24-5x$

Now we divide both sides by -4

$y=-6+1.25x$

Now we are told that a dilation by a factor of 0.2 occurs. Since dilation doesn't affect the slope of lines, this means that the equation of the image line has the same slope, that is 1.25. The point that will be affected is the y-intercept, that is (0,-6). Since the image of a point after dilation is the following:

$(x^{\prime},y^{\prime})=(kx,ky)$

Applying this to the y-intercept point we get:

$(x^{\prime},y^{\prime})=(0,(0.2)(-6))=(0,-1.2)$

Therefore, the equation of the line image is:

$y=-1.2+1.25x$