Math Problem Statement

Consider the equation y = -x + 5. Fill in the blanks to complete the table of values for x = -1, 0, 1, and 2.

Solution

To complete the table of values for the equation y=−x+5y = -x + 5, let's substitute each value of xx into the equation and solve for yy.

The given values of xx are: -1, 0, 1, and 2.

  1. When x=−1x = -1: y=−(−1)+5=1+5=6y = -(-1) + 5 = 1 + 5 = 6

  2. When x=0x = 0: y=−(0)+5=0+5=5y = -(0) + 5 = 0 + 5 = 5

  3. When x=1x = 1: y=−(1)+5=−1+5=4y = -(1) + 5 = -1 + 5 = 4

  4. When x=2x = 2: y=−(2)+5=−2+5=3y = -(2) + 5 = -2 + 5 = 3

So, the completed table of values should look like this:

x & y \\ \hline -1 & 6 \\ 0 & 5 \\ 1 & 4 \\ 2 & 3 \\ \end{array}$$ Would you like any further details or have any questions? Here are five related questions to expand your understanding: 1. How would the values change if the equation was $$y = x + 5$$ instead? 2. What happens to the graph of $$y = -x + 5$$ if the +5 is replaced by another constant, say +3? 3. How does changing the slope (the coefficient of $$x$$) affect the line on a graph? 4. What would the table look like for a different range of $$x$$ values, like -2, 1, 3, and 4? 5. Can you identify the y-intercept of the equation $$y = -x + 5$$ from this table? **Tip:** The value of $$y$$ when $$x = 0$$ is always the y-intercept of a linear equation in the form $$y = mx + b$$.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing

Formulas

y = mx + b

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 7-9

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