Line l has the equatin y= 1/3x. find the equation of the image l after a dilation with a scale factor of 1/2, centered at the origin.

Step-by-step explanation:

The equation of the line I is  

Scale factor = , center = (0, 0)

To find the dilated line, we need follow the steps below:

Step 1: Draw the equation of the given line I

Step 2: Let's take a point from the line.

Let's take (2, 6) which is on the line I.

Let's find the dilated point by the scale factor  

Multiply the point (2, 6) by  , we get

( = (1, 3)

Step 3: Write the equation of the new line (Image I)

The dilated line has the same slope.

So slope (m) =  

x = 1 and y = 3

Now let's find the slope intercept.

y = mx + b

Plug in x = 1, y = 3 and slope (m) =  

3 =  .1 + b

3 = + b

b = 3 -

b =

Now let's find the equation of the image I.

y = mx + b

The required equation is after the dilation of scale factor.

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