draw the graph of y=2x for the value of x from -5 to 5. using transformation Also draw the graph of y=2x-3

Here are the graphs for the equations \( y = 2x \) and \( y = 2x - 3 \) for \( x \) values ranging from -5 to 5.

- The blue line represents \( y = 2x \).
- The red line represents \( y = 2x - 3 \).

The graph of \( y = 2x - 3 \) is obtained by shifting the graph of \( y = 2x \) downward by 3 units. This transformation is a vertical translation.

Would you like further details or have any questions?

Here are some related questions:
1. How would the graph change if the equation were \( y = 2x + 3 \)?
2. What effect does multiplying \( x \) by a constant (e.g., \( y = 3x \)) have on the graph?
3. How does the graph of \( y = -2x \) compare with \( y = 2x \)?
4. What would happen if we added a horizontal shift, like \( y = 2(x - 1) \)?
5. How does changing the slope (coefficient of \( x \)) affect the steepness of the graph?

**Tip:** In transformations, vertical shifts change the \( y \)-intercept, while horizontal shifts change where the line crosses the \( x \)-axis.

Understand how to graph the linear equations y = 2x and y = 2x - 3 over the range of x values from -5 to 5. Learn about graph transformations, including vertical shifts, and how they affect the slope and y-intercept of a line. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation