John Newton
09/26/2023 · Elementary School
Write an equation for each transformation of \( y=x \) \( \begin{array}{ll}\text { 19. Vertical stretch by a factor of } 9 & \text { 20. } 3 \text { units up }\end{array} \)
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Step-by-step Solution
To transform the equation \( y = x \) according to the specified transformations, we can apply the following steps:
19. **Vertical stretch by a factor of 9**: To vertically stretch the graph of \( y = x \) by a factor of 9, we multiply the output (y-value) by 9. The equation becomes:
\[
y = 9x
\]
20. **3 units up**: To move the graph of \( y = x \) up by 3 units, we add 3 to the output (y-value). The equation becomes:
\[
y = x + 3
\]
So, the equations for the transformations are:
- For the vertical stretch by a factor of 9: \( y = 9x \)
- For moving 3 units up: \( y = x + 3 \)
Quick Answer
- For the vertical stretch by a factor of 9: \( y = 9x \)
- For moving 3 units up: \( y = x + 3 \)
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