Math Problem Statement

y=2x+1-2 What is the transformation?

A.Vertical Translation up 2 and Horizontal translation right 1

B. Vertical Translation down 2 and Horizontal Translation left 1

C.Horizontal Translation left 2 and Vertical Translation up 1

D.Horizontal Translation right 2 and Vertical Translation down 1

Solution

Let's first rewrite the equation y=2x+12y = 2x + 1 - 2 to make it clearer:

y=2x1y = 2x - 1

This equation represents a linear function of the form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.

Now let's analyze any transformations:

  • Horizontal Translation: There are no parentheses involving xx, meaning no shift left or right.
  • Vertical Translation: The y-intercept changes from 0 (for y=2xy = 2x) to 1-1. This is a shift down by 1 unit.

Final Answer:

The correct option is:

None of the listed options exactly fit.

Explanation:

  • There is only a vertical translation down by 1 unit.
  • No horizontal translation occurs because the equation is not written in a shifted form like y=2(xh)+ky = 2(x - h) + k.

Would you like more details or have other questions?


Here are 5 related questions to expand your knowledge:

  1. How do horizontal translations differ from vertical translations in linear equations?
  2. What happens when you multiply the slope mm by a negative value?
  3. How does the equation y=2(x2)+3y = 2(x - 2) + 3 transform compared to y=2xy = 2x?
  4. What is the general form of a linear equation involving both horizontal and vertical shifts?
  5. Can you identify the slope and y-intercept from the equation y=3x4y = 3x - 4?

Tip: Always look for parentheses involving xx to spot horizontal translations directly!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Transformations
Vertical Translations

Formulas

y = mx + b (Slope-Intercept Form)

Theorems

Linear transformation theorem

Suitable Grade Level

Grades 8-10