Quicly the equation 8x - 4y = 5 is dilated by a scale factor of 8 centered at the origin. what is the new slope and y-intercept after dilation?

For new line, slope m=2 and y-intercept c=(-10)

Step-by-step explanation:

Note : Figure given is for reference to understand better.

Where redline is for given line and blueline for new line

The equation of given line 8x-4y=5 and it is dilated by a scale factor of 8 centered at the origin.

Step 1 : Find two points on given line.

When x=0, y=?

When y=0, x=?

We get points

Step 2: Find distance from centered and scale it.

Now, It is said that line 8x-4y=5 dilated by a scale factor of 8 centered at the origin and point A and point B is on same.

So that point A and point B  will also get dilated by a scale factor of 8 centered at the origin or distance of points from origin will be scaled by 8.

For point A:

Distance of point from origin is  unit in x-direction and zero  unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is

For point B:

Distance of point from origin is unit in x-direction and zero unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is

Step 3: Find Equation of new line.

Points and make a new line

The equation of given as

Now, Comparing with the equation of the line : y=mx + c

Where m=slope and c is the y-intercept

We get, Slope m=2 and y-intercept c=(-10)

the correct answer is d

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