How is the graph of y=2x−1𝑦=2𝑥−1 transformed from y=2x𝑦=2𝑥?Horizontal shift Answer 1 Question 3 Answer 2 Question 3 unit(s).

To analyze the transformation of the graph of $y = 2x - 1$ from $y = 2x$, we need to identify the specific changes in the equation.

1. ### Break Down the Problem

1. Identify the original equation: $y = 2x$.
2. Identify the transformed equation: $y = 2x - 1$.
3. Determine the transformation involved (vertical shift, horizontal shift, reflection, and stretch).

2. ### Relevant Concepts

• The equation $y = mx + b$ represents a linear function where:
  • $m$ is the slope,
  • $b$ is the y-intercept.
• A change in $b$ indicates a vertical transformation.

3. ### Analysis and Detail

• The original equation $y = 2x$ has a slope of $2$ and a y-intercept at $(0,0)$.
• In the transformed equation $y = 2x - 1$:
  • The slope remains $2$,
  • The y-intercept is now $-1$, which means the graph shifts downward by 1 unit.

4. ### Verify and Summarize

• The transformation is a vertical shift downwards.
• There is no horizontal shift involved, as the $x$-term remains unchanged in structure (it is still $2x$).

Final Answer

The graph of $y = 2x - 1$ is transformed from $y = 2x$ by a vertical shift downwards by 1 unit. There is no horizontal shift.