Write an equation for the transformation of y=x.
vertical stretch by a factor of 2
The equation for the vertical stretch of y=x by a factor of 2 can be written as y = 2x.
To represent the given transformation of a vertical stretch by a factor of 2 for the equation y = x, we can introduce a scaling factor of 2 to the equation. This can be done by multiplying the variable x by 2. Therefore, the equation for the transformed function is:
y = 2x
To write an equation representing the transformation of y = x with a vertical stretch by a factor of 2, you would need to modify the equation to stretch the y-values. Here's how you can do it:
1. Start with the equation y = x. This represents a straight line with a slope of 1 passing through the origin.
2. To stretch the y-values vertically by a factor of 2, multiply the y-values by 2. This will make the line appear twice as tall.
3. The new equation would be y = 2x. This equation represents a straight line with a slope of 2 passing through the origin. Every point on the line would have a corresponding y-value that is twice the value of its original position on the y-axis.
Thus, the equation for the transformation of y = x with a vertical stretch by a factor of 2 is y = 2x.