Question

The graph of the line has an equation of y = 5x - 8. What is the equation of the line after a dilation with a scale factor of 3 2 , centered at the origin. A) y = 5x - 6 B) y = 5x - 12 C) y = 15 2 x - 8 D) y = 15 2 x - 12

Answer 1

The correct option is B.

Explanation:

The given equation of line is

`y=5x-8` .... (1)

The slope intercept form of a line is

`y=mx+b` ..... (2)

where, m is slope and b is y-intercept.

From (1) and (2), we get

`m=5,b=-8`

It means the slope of line is 5 and y-intercept is at (0,-8).

If a line dilated with a scale factor of 3/2 centered at the origin, then the slope of both lines are same and the relation between coordinates is

`(x,y)\rightarrow((3)/(2)x, (3)/(2)y)`

`(0,-8)\rightarrow((3)/(2)(0), (3)/(2)(-8))=(0,-12)`

The slope of dilated line is 5 and the y-intercept is at (0,-12). So, the equation of dilated line is

`y=5x-12`

Therefore option B is correct.

Answer 2

B) y = 5x -12

Explanation:

Dilation changes the distance of points from the origin, but does not change angles (slopes of lines). Hence the y-intercept moves from -8 to 3/2·(-8) = -12, but the slope stays the same.