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Find A, B, C by Completing the Table for Linear Equation y = -2x -1
Mathematics
Grade 8
Question Content
Copy and complete the table of values for $y = -2x - 1$. What values should replace A, B and C? The table has x values: -2, -1, 0, 1, 2 and corresponding y values: 3, A, B, -3, C.
Correct Answer
A = 1, B = -1, C = -5
Detailed Solution Steps
1
Step 1: Solve for A (when x = -1): Substitute x = -1 into the equation $y = -2x - 1$. Calculate $y = -2(-1) - 1 = 2 - 1 = 1$, so A = 1.
2
Step 2: Solve for B (when x = 0): Substitute x = 0 into the equation $y = -2x - 1$. Calculate $y = -2(0) - 1 = 0 - 1 = -1$, so B = -1.
3
Step 3: Solve for C (when x = 2): Substitute x = 2 into the equation $y = -2x - 1$. Calculate $y = -2(2) - 1 = -4 - 1 = -5$, so C = -5.
Knowledge Points Involved
1
Linear Function Substitution
This refers to replacing the independent variable (x) in a linear equation $y=mx+b$ with a given value, then performing arithmetic operations to find the corresponding dependent variable (y) value. It is the core method for generating tables of values for linear relationships, used to graph lines or verify solutions to linear equations.
2
Integer Multiplication with Negative Numbers
The rule states that multiplying two negative numbers gives a positive product, while multiplying a positive and a negative number gives a negative product. For example, $-2(-1)=2$ and $-2(2)=-4$. This is essential for accurate calculations when substituting negative x-values into linear equations.
3
Evaluating Linear Equations
This is the process of computing the output (y) of a linear equation $y=mx+b$ for a specific input (x). It requires following the order of operations (PEMDAS/BODMAS): first perform multiplication/division, then addition/subtraction. It is used to analyze linear relationships, create data tables, and plot linear graphs.
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