Question

Line has the equation y= – 1/ 3 x–3. Write the equation of the image of after a dilation with a scale factor of 3, centered at the origin. Write your answer in slope-intercept form.

Answer 1

Answer:

The the equation of the image of after a dilation with a scale factor of 3, centered at the origin will be $y=\:-\:\frac{1}{3}x-9$, which is shown as blue colored line in attached graph.

Step-by-step explanation:

Considering the equation of the line

$y=\:-\:\frac{1}{3}x-3$

Comparing with the slope-intercept form $y = mx + b$, we can determine that the slope of line is $m = \frac{-1}{3}$, as shown in the attached figure. The red colored line indicated the this (original) line.

We have to write the equation of the image after a dilation with a scale factor of 3, centered at the origin.

Writing Steps:

• First draw the line of the equation as shown in attached figure.

• Then take a point from the line. Let suppose the point is (0, -3).

• Then dilate the point (0, -3) with a scale factor of 3 by multiplying the coordinates of the point (0, -3) with 3 to determine the location of the dilated point. So,

(x, y)     ⇒     (3x, 3y)

(0, -3)   ⇒      (3×0, 3×-3) = (0, -9)

Now, lets write the equation of new line

As the dilated line has same slope. So,

$m = \frac{-1}{3}$

As the dilated point is  (0, -9), in which

x = 0, and y = -9

As the slope-intercept form is

$y = mx + b$  where  $m = \frac{-1}{3}$

So, putting the values in slope intercept form

$y = mx + b$

$-9=\:-\:\frac{1}{3}\left(0\right)+b$

$\mathrm{Switch\:sides}$

$-\frac{1}{3}\left(0\right)+b=-9$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$-\frac{1}{3}\cdot \:0+b=-9$

$\mathrm{Apply\:rule}\:0\cdot \:a=0$

$-0+b=-9$

$b=-9$

So, the equation of image becomes

$y=\:-\:\frac{1}{3}x+\left(-9\right)$

$y=\:-\:\frac{1}{3}x-9$

So, the the equation of the image of after a dilation with a scale factor of 3, centered at the origin will be $y=\:-\:\frac{1}{3}x-9$, which is shown as blue colored line in attached graph.

Keywords: equation, dilation, scale factor of 3

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