Question

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.

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer:

$y = \frac{1}{3} x + \frac{8}{3}$

Step-by-step explanation:

The equation of the line I is  $y = \frac{1}{3} x$

Scale factor = $\frac{1}{2}$, 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  $\frac{1}{2}$

Multiply the point (2, 6) by  $\frac{1}{2}$, we get

($2.\frac{1}{2} , 6.\frac{1}{2} )$ = (1, 3)

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

The dilated line has the same slope.

So slope (m) =  $\frac{1}{3}$

x = 1 and y = 3

Now let's find the slope intercept.

y = mx + b

Plug in x = 1, y = 3 and slope (m) =  $\frac{1}{3}$

3 =  $\frac{1}{3}$.1 + b

3 = $\frac{1}{3}$ + b

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

b = $\frac{3.3 -1}{3} = \frac{9 -1}{3} = \frac{8}{3}$

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

y = mx + b

$y = \frac{1}{3} x + \frac{8}{3}$

The required equation is $y = \frac{1}{3} x + \frac{8}{3}$ after the dilation of scale factor.