Question

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?

Answer 1

The correct equation for the dilated line is y = 1/3x + 18.

Step-by-step explanation:

In order to determine who is correct, we need to apply the dilation to the original equation and see if it matches either of the proposed equations.

The dilation with a center at the origin and a scale factor of 6 means that the x-values are multiplied by 1/6 and the y-values are multiplied by 6.

Applying this dilation to y = 2x + 3, we get y = 2(1/6x) + 3(6), which simplifies to y = 1/3x + 18. Therefore, neither Ava nor Sarena's equations are correct. The correct equation for the dilated line is y = 1/3x + 18.