Math Problem Statement

Complete the table and graph the equation y = -x + 1.

Solution

Part (a): Completing the table for the graph of y=−x+1y = -x + 1

To fill in the missing values for AA and BB, we substitute the given values of xx into the equation y=−x+1y = -x + 1.

  1. For x=−2x = -2: y=−(−2)+1=2+1=3y = -(-2) + 1 = 2 + 1 = 3 So, A=3A = 3.

  2. For x=1x = 1: y=−(1)+1=−1+1=0y = -(1) + 1 = -1 + 1 = 0 So, B=0B = 0.

The completed table is:

\hline x & -2 & -1 & 0 & 1 & 2 \\ \hline y & 3 & 2 & 1 & 0 & -1 \\ \hline \end{array}$$ ### Part (b): Graph of $$y = -x + 1$$ For graphing the line $$y = -x + 1$$, we can plot the points from the completed table: - $$(-2, 3)$$ - $$(-1, 2)$$ - $$(0, 1)$$ - $$(1, 0)$$ - $$(2, -1)$$ Plot these points on the given axes and connect them to form a straight line. Would you like to ask more questions about this or need any clarification? Here are five questions you can explore further: 1. What is the slope of the line $$y = -x + 1$$? 2. How does changing the equation to $$y = -x + 2$$ affect the graph? 3. Can you find the x-intercept and y-intercept from the equation $$y = -x + 1$$? 4. How would the graph look if the equation was $$y = x + 1$$ instead? 5. What is the domain and range of the function $$y = -x + 1$$? **Tip:** The slope in the equation $$y = -x + 1$$ is the coefficient of $$x$$, which tells you how the graph behaves (in this case, it has a negative slope).

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing
Slope-Intercept Form

Formulas

y = mx + b (Slope-Intercept Form)
y = -x + 1

Theorems

Linearity of Functions

Suitable Grade Level

Grades 7-10

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