Math Problem Statement

Copy and complete the table for the graph y = -2x - 1. What values should replace A, B, and C?

Solution

The equation provided is y=2x1y = -2x - 1. You are asked to complete the table with missing values for yy corresponding to different values of xx.

Let's substitute the given xx values into the equation y=2x1y = -2x - 1 to find the missing values:

  1. For x=2x = -2: y=2(2)1=41=3y = -2(-2) - 1 = 4 - 1 = 3 So the value for yy when x=2x = -2 is 3, which matches the table.

  2. For x=1x = -1 (finding A): y=2(1)1=21=1y = -2(-1) - 1 = 2 - 1 = 1 So, A=1A = 1.

  3. For x=0x = 0 (finding B): y=2(0)1=01=1y = -2(0) - 1 = 0 - 1 = -1 So, B=1B = -1.

  4. For x=1x = 1: y=2(1)1=21=3y = -2(1) - 1 = -2 - 1 = -3 This matches the table.

  5. For x=2x = 2 (finding C): y=2(2)1=41=5y = -2(2) - 1 = -4 - 1 = -5 So, C=5C = -5.

The completed table is:

x & -2 & -1 & 0 & 1 & 2 \\ \hline y & 3 & 1 & -1 & -3 & -5 \\ \end{array}$$ Do you want any further details or clarifications? Here are five related questions to deepen your understanding: 1. What is the slope of the graph $$y = -2x - 1$$? 2. How would you graph this equation based on the table of values? 3. What is the y-intercept of the equation $$y = -2x - 1$$? 4. How does changing the slope affect the graph of a line? 5. What happens to the graph if the constant term changes from $$-1$$ to a different value? **Tip**: The slope of the equation tells you how much $$y$$ changes for each unit change in $$x$$.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear Equations
Substitution
Graphing

Formulas

y = mx + b
Substitution for different x values

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 6-8