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

The equation of line L is

`y = 3x + (16)/(9)`

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 = (8)/(4.5)`

`b = (16)/(9)`

The equation of line L is of the form:

`y = mx + b`

We substitute to get;

`y = 3x + (16)/(9)`