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Line L is mapped onto line m by a dilation centered at the origin with a scale factor of 4.5. Line m is represented by y=3x+8 and it passes through the lint whose coordinates are (-4,-4).

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Answer:

The equation of line L is

[tex]y = 3x + \frac{16}{9} [/tex]

Step-by-step explanation:

Assuming we want to find the equation of line L.

The equation of line M is

[tex]y = 3x + 8[/tex]

and it passes through (-4,-4). This line was obtained after a dilation of line M by a scale factor of 4.5.

The slope of both lines are the same.

Therefore line L also has slope

[tex]m = 3[/tex]

We need to obtain the y-intercept of line L. We divide the y-intercept of line M by 4.5 to get that of line L.

[tex]b = \frac{8}{4.5} [/tex]

[tex]b = \frac{16}{9} [/tex]

The equation of line L is of the form:

[tex]y = mx + b[/tex]

We substitute to get;

[tex]y = 3x + \frac{16}{9} [/tex]

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