Consider the line y=x.
a. If the line is dilated by a factor of 2, what is the equation of the resulting line?
b. If the resulting line is translated 3 units up, what is the equation of the resulting line?
my answers:
a. y = 2x
b. y = 2x + 3
am i right?
Your answer for a. is right, but b. is incorrect.
Nevermind, sorry. Both are correct.
Yes, you are correct in your answers.
a. When the line y = x is dilated by a factor of 2, it means that every point on the original line is multiplied by 2. This includes both the x-coordinate and the corresponding y-coordinate. Therefore, the equation of the resulting line will be y = 2x.
b. After the resulting line is translated 3 units up, it means that all the y-values of the points on the line are increased by 3. Since the equation of the resulting line after dilation is y = 2x, adding 3 to the y-values will give the equation y = 2x + 3.