Math Problem Statement

Consider the equation y = -4x + 10. Fill in the blanks to complete the table of values for x = -1, 1, 3, 5.

Solution

To complete the table for the equation y=−4x+10y = -4x + 10, let’s substitute each xx-value and calculate the corresponding yy-value:

  1. For x=−1x = -1: y=−4(−1)+10=4+10=14y = -4(-1) + 10 = 4 + 10 = 14

  2. For x=1x = 1: y=−4(1)+10=−4+10=6y = -4(1) + 10 = -4 + 10 = 6

  3. For x=3x = 3: y=−4(3)+10=−12+10=−2y = -4(3) + 10 = -12 + 10 = -2

  4. For x=5x = 5: y=−4(5)+10=−20+10=−10y = -4(5) + 10 = -20 + 10 = -10

So, the completed table is:

\hline x & y \\ \hline -1 & 14 \\ 1 & 6 \\ 3 & -2 \\ 5 & -10 \\ \hline \end{array}$$ Would you like further details on how these calculations were performed? Here are some additional questions that could help expand your understanding: 1. What is the slope of the line represented by the equation $$y = -4x + 10$$? 2. How does changing the $$y$$-intercept affect the graph of this line? 3. How would the values change if the equation were $$y = 4x + 10$$ instead? 4. What does a negative slope indicate about the direction of the line? 5. Can you predict the $$y$$-value for $$x = 7$$ using this equation? **Tip:** In linear equations, the slope determines the steepness and direction of the line, while the intercept dictates where it crosses the $$y$$-axis.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Substitution
Coordinate Points

Formulas

y = mx + b

Theorems

-

Suitable Grade Level

Grades 7-9

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