Question

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).

Answer 1

Answer:

The equation of line L is

$y = 3x + \frac{16}{9}$

Step-by-step explanation:

Assuming we want to find the equation of line L.

The equation of line M is

$y = 3x + 8$

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

$m = 3$

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.

$b = \frac{8}{4.5}$

$b = \frac{16}{9}$

The equation of line L is of the form:

$y = mx + b$

We substitute to get;

$y = 3x + \frac{16}{9}$