A line with the equation y = 2x +3 is dilated with the center of the dilation at the origin and a scale factor of 6. Ava believes the equation of the image line will be y=12x+4 while her friend Sarena believes the equation is y = 2x +18. Is one of them correct? If so, who is it and why? If not, why are they both wrong?

Respuesta :

Given the equation before dilation as y = 2x+3

Before we dilate, we need to get the x and y intercept of the line as shown;

when x = 0;

y = 2(0)+3

y = 3

The coordinate point is (0, 3)

When y = 0

0 = 2x-3

-2x = -3

x = 3/2

The coordinate point is (3/2 , 0)

If this coordinates is dialated by a factor of 6, the coordinates becomes;

(6*0, 6*3) and (6*3/2, 0*6)

= (0, 18) and (9, 0)

Looking for the equation of the resulting coordinate;

slope m = 0-18/9-0

slope m = -18/9 = -2

Get the inercept. Substitutte (0, 18) and m = -2 into the equation y = mx+c

18 = -2(0)+ c

c = 18

Get the required equation;

y = mx+c

y = -2x + 18

They are both wrong, the slope of Serena is 2 instead of -2 even though her intercept value is correct while Ava is also wrong because the slope and intercept of the dilated coordinate are wrong

ACCESS MORE
EDU ACCESS