Consider the line y=x.
If the line is dilated by a factor of 2, what is the equation of the resulting line?
If the resulting line is translated 3 units up, what is the equation of the resulting line?
Please answer!~
a. What is the difference between y=x and y=2x ?
b. what happens to y=x when one adds 4, as in y=x+4
and
Step-by-step explanation:
When we dilate y = x by a factor of "a", we have the equation:
y = a*x
So, firstly, we need to dilate by a factor of 1/3, thus we would have:
Now, whenever we have a line y = x, per say, if we want to translate "b" units up, we would have:
y = x + b
if we want to translate "b" units down, we have"
y = x - b
Now, since we have and we want to translate "1" unit down, we will thus have:
help i'm still so confused
To find the equation of the resulting line after dilation, we need to multiply the coefficients of x and y by the scale factor.
The equation of the line y = x represents a line with a slope of 1. If we want to dilate this line by a factor of 2, we need to multiply the coefficients of x and y by 2.
Therefore, the resulting line after dilation will have an equation of y = 2x.
Now, to find the equation of the resulting line after translation, we need to shift the line vertically by a certain number of units. In this case, we want to move the line 3 units up.
To achieve this, we need to add 3 to the y-intercept of the transformed line. Since the original line y = 2x has a y-intercept of 0, the new y-intercept will be 0 + 3 = 3.
So, the equation of the resulting line after dilation and translation will be y = 2x + 3.