Answer:
[tex]\displaystyle y=\frac{1}{3}x-6[/tex]
Step-by-step explanation:
Dilation of a Line
Given a line that passes through points A(-3,-4) and B(-6,-5). We'll apply a dilation with a scale factor of 2 centered at the origin by multiplying each coordinate by 2. The points map to:
A'(-6,-8) and B'(-12,-10)
Now we find the equation of the line passing through A' and B'.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Substituting:
[tex]\displaystyle y+8=\frac{-10+8}{-12+6}(x+6)[/tex]
[tex]\displaystyle y+8=\frac{-2}{-6}(x+6)[/tex]
[tex]\displaystyle y+8=\frac{1}{3}(x+6)[/tex]
Operating:
[tex]\displaystyle y=\frac{1}{3}x+\frac{1}{3}*6-8[/tex]
[tex]\displaystyle y=\frac{1}{3}x+2-8[/tex]
[tex]\boxed{\displaystyle y=\frac{1}{3}x-6}[/tex]
