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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 :

sqdancefan

Answer:

B) y = 5x -12

Step-by-step 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.

Answer:

The correct option is B.

Step-by-step explanation:

The given equation of line is

[tex]y=5x-8[/tex]           .... (1)

The slope intercept form of a line is

[tex]y=mx+b[/tex]        ..... (2)

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

From (1) and (2), we get

[tex]m=5,b=-8[/tex]

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

[tex](x,y)\rightarrow(\frac{3}{2}x, \frac{3}{2}y)[/tex]

[tex](0,-8)\rightarrow(\frac{3}{2}(0), \frac{3}{2}(-8))=(0,-12)[/tex]

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

[tex]y=5x-12[/tex]

Therefore option B is correct.

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