Please helppp, I'm using all my points!! Line A passes through the points (-3,-4) and (-6,-5). Write the equation of the image of A after a dilation with a scale factor of 2. Write your in answer in slope-intercept form. y=

The equation of the image of A after a dilation with a scale factor of 2 will be:

Step-by-step explanation:

Some background Knowledge about dilation.

We know that when an object is dilated by a scale factor, it gets reduced, stretched, or remains the same, depending upon the value of the scale factor.

Rule to calculate the dilation by a scale factor 2 centered at the origin

P(x, y) → P'(2x, 2y)

Here, P'(2x, 2y) is the image of P(x, y).

Now, let us solve our case:

Given the points

Let say the points are X(-3, -4) and Y(-6, -5)

Rule to calculate the dilation by a scale factor 2 centered at the origin

P(x, y) → P'(2x, 2y)

so

X(-3, -4)    →   X' (2(-3), 2(-4))    →    X'(-6, -8)

Y(-6, -5)    →   Y' (2(-6), 2(-5))    →    Y'(-12, -10)

Thus, after the dilation scale of factor 2, now the image line will through the points X'(-6, -8) and Y'(-12, -10)

so we have the points of the image line

Determining the slope between X'(-6, -8) and Y'(-12, -10)

The slope-intercept form of the line equation

y = mx+b

where

now substituting m = 1/3 and (-6, -8) in the slope-intercept form of the line equation

Add 3 to both sides

Simplify

now substituting b = -6 and m = 1/3 in the slope-intercept form of line equation

Therefore, the equation of the image of A after a dilation with a scale factor of 2 will be:

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step-by-step explanation: