Math Problem Statement

Compare the graphs of the given linear equations: y = x + 2 and y = x - 2, as well as y = x + 1/3 and y = 1/3x. Complete the statements regarding their slopes, y-intercepts, and graph transformations.

Solution

The image you've uploaded contains a problem from the ALEKS system, which involves comparing linear functions and their graphs. The problem asks you to complete the statements about the graphs of the following equations:

  1. y = x + 2 and y = x - 2
  2. y = x + 1/3 and y = 1/3x

The questions are about how these equations compare in terms of their slopes, y-intercepts, and behavior on the graph. However, the full information regarding the questions and choices is not fully visible.

Would you like to provide more details or ask specific questions about these functions? I can help break them down and explain the differences between these linear equations. Let me know if you need further assistance.

Here are some related questions that could help expand on this topic:

  1. How do you determine the slope and y-intercept of a linear equation from its graph?
  2. What is the difference between y = mx + b and y = x + b?
  3. How do you graph the line y = x + 2 and y = x - 2?
  4. What does the slope of a line tell you about the function's rate of change?
  5. How do vertical and horizontal shifts of a graph affect its equation?

Tip: To find the y-intercept of a linear equation like y = mx + b, simply set x = 0 and solve for y.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear Equations
Graph Transformations
Slope-Intercept Form

Formulas

y = mx + b (Slope-Intercept Form)

Theorems

Slope Theorem
Y-Intercept Theorem

Suitable Grade Level

Grades 8-10