Consider the line y = x . If the line is dilated by a factor of 1/3 , what is the equation of the resulting line? If the resulting line is translated 1 unit down, what is the equation of the resulting line?
What's the answer
What’s the answer??!
To find the equation of the resulting line after dilating the line y = x by a factor of 1/3, we need to multiply both the x and y coordinates by 1/3.
Let's start by considering a point on the original line, (x, y). After the dilation, the coordinates of this point will become (1/3 * x, 1/3 * y).
Since the equation of the original line is y = x, we substitute the new coordinates into this equation:
1/3 * y = 1/3 * x.
To simplify, we can multiply both sides of the equation by 3 to get:
y = x.
This means that the equation of the resulting line after dilation is y = x.
Now, let's consider the translation of the resulting line 1 unit down. To do this, we simply subtract 1 from the y-coordinate of every point on the line.
The equation of the resulting line will be y = x - 1.
So, after dilating the line y = x by a factor of 1/3 and translating it 1 unit down, the equation of the resulting line is y = x - 1.