Math Problem Statement

Copy and complete the table below for the graph of y = -x + 1 and draw the graph on the provided axes.

Solution

Let's work through this step-by-step.

Part (a): Completing the Table for y=−x+1y = -x + 1

The equation given is: y=−x+1y = -x + 1

To find the missing values AA and BB, substitute the xx-values into the equation.

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

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

The completed table should be:

\hline x & -2 & -1 & 0 & 1 & 2 \\ \hline y & 3 & 2 & 1 & 0 & -1 \\ \hline \end{array}$$ ### Part (b): Drawing the Graph of $$y = -x + 1$$ To graph $$y = -x + 1$$, plot the points from the table: - $$(-2, 3)$$ - $$(-1, 2)$$ - $$(0, 1)$$ - $$(1, 0)$$ - $$(2, -1)$$ These points form a straight line with a negative slope of $$-1$$, as indicated by the equation. Connect these points to complete the graph. Would you like more details on the graphing process, or do you have any questions? --- ### Related Questions 1. How would the graph change if the equation were $$y = -2x + 1$$? 2. What does the slope of $$-1$$ tell us about the graph? 3. How can we verify that our points lie on the line $$y = -x + 1$$? 4. What is the y-intercept of the line $$y = -x + 1$$, and what does it represent? 5. How would you find the x-intercept of this line? ### Tip When graphing linear equations, always check the y-intercept (where $$x = 0$$) and use the slope to find additional points easily.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing
Coordinate Points

Formulas

y = -x + 1

Theorems

-

Suitable Grade Level

Grades 6-8

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