Complete the tables below. Note the inclusion of decimal and fractional values as per senior phase requirements. Using the skill of algebraic substitution, calculate the output values for the following linear equations.

Mathematics
Complete the tables below. Note the inclusion of decimal and fractional values as per senior phase requirements. Using the skill of algebraic substitution, calculate the output values for the following linear equations.

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Answer

1.5

Task 1.1: Complete the tables

Equation 1: y=12x+2y = \frac{1}{2}x + 2

Step 1: Calculate output (y) values for Equation 1. • For x=−2x = -2: y=12(−2)+2=−1+2=1y = \frac{1}{2}(-2) + 2 = -1 + 2 = 1 • For x=−1x = -1: y=12(−1)+2=−0.5+2=1.5y = \frac{1}{2}(-1) + 2 = -0.5 + 2 = 1.5 • For x=0x = 0: y=12(0)+2=0+2=2y = \frac{1}{2}(0) + 2 = 0 + 2 = 2 • For x=0.5x = 0.5: y=12(0.5)+2=0.25+2=2.25y = \frac{1}{2}(0.5) + 2 = 0.25 + 2 = 2.25 • For x=2x = 2: y=12(2)+2=1+2=3y = \frac{1}{2}(2) + 2 = 1 + 2 = 3

Step 2: Complete the table for Equation 1.

Input(x)−2−100.52Output(y)11.522.253OrderedPair(x;y)(−2;1)(−1;1.5)(0;2)(0.5;2.25)(2;3)\begin{array}{|c|c|c|c|c|c|} \hline Input (x) & -2 & -1 & 0 & 0.5 & 2 \\ \hline Output (y) & 1 & 1.5 & 2 & 2.25 & 3 \\ \hline Ordered Pair (x; y) & (-2; 1) & (-1; 1.5) & (0; 2) & (0.5; 2.25) & (2; 3) \\ \hline \end{array}

Show your substitution calculations for Equation 1 when:

Step 3: Calculate for x=−1x = -1.

y=12x+2y=12(−1)+2y=−12+2y=−0.5+2y=1.5\begin{align*} y &= \frac{1}{2}x + 2 \\ y &= \frac{1}{2}(-1) + 2 \\ y &= -\frac{1}{2} + 2 \\ y &= -0.5 + 2 \\ y &= \textbf{1.5} \end{align*}

Step 4: Calculate for x=2x = 2.

y=12x+2y=12(2)+2y=1+2y=3\begin{align*} y &= \frac{1}{2}x + 2 \\ y &= \frac{1}{2}(2) + 2 \\ y &= 1 + 2 \\ y &= \textbf{3} \end{align*}

Equation 2: y=2x−4y = 2x - 4

Step 5: Calculate output (y) values for Equation 2. • For x=−2x = -2: y=2(−2)−4=−4−4=−8y = 2(-2) - 4 = -4 - 4 = -8 • For x=−1x = -1: y=2(−1)−4=−2−4=−6y = 2(-1) - 4 = -2 - 4 = -6 • For x=0x = 0: y=2(0)−4=0−4=−4y = 2(0) - 4 = 0 - 4 = -4 • For x=0.5x = 0.5: y=2(0.5)−4=1−4=−3y = 2(0.5) - 4 = 1 - 4 = -3 • For x=2x = 2: y=2(2)−4=4−4=0y = 2(2) - 4 = 4 - 4 = 0

Step 6: Complete the table for Equation 2.

Input(x)−2−100.52Output(y)−8−6−4−30OrderedPair(x;y)(−2;−8)(−1;−6)(0;−4)(0.5;−3)(2;0)\begin{array}{|c|c|c|c|c|c|} \hline Input (x) & -2 & -1 & 0 & 0.5 & 2 \\ \hline Output (y) & -8 & -6 & -4 & -3 & 0 \\ \hline Ordered Pair (x; y) & (-2; -8) & (-1; -6) & (0; -4) & (0.5; -3) & (2; 0) \\ \hline \end{array}

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Quick Answer

Task 1.1: Complete the tables Equation 1: y = (1)/(2)x + 2 Step 1: Calculate output (y) values for Equation 1.

Complete the tables below. Note the inclusion of decimal and fractional values as per senior phase requirements. Using the skill of algebraic substitution, calculate the output values for the following linear equations.
Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI Answer
Task 1.1: Complete the tables Equation 1: y = (1)/(2)x + 2 Step 1: Calculate output (y) values for Equation 1. • For x = -2: y = (1)/(2)(-2) + 2 = -1 + 2 = 1 • For x = -1: y = (1)/(2)(-1) + 2 = -0.5 + 2 = 1.5 • For x = 0: y = (1)/(2)(0) + 2 = 0 + 2 = 2 • For x = 0.5: y = (1)/(2)(0.5) + 2 = 0.25 + 2 = 2.25 • For x = 2: y = (1)/(2)(2) + 2 = 1 + 2 = 3 Step 2: Complete the table for Equation 1. |c|c|c|c|c|c| Input (x) & -2 & -1 & 0 & 0.5 & 2 \\ Output (y) & 1 & 1.5 & 2 & 2.25 & 3 \\ Ordered Pair (x; y) & (-2; 1) & (-1; 1.5) & (0; 2) & (0.5; 2.25) & (2; 3) \\ Show your substitution calculations for Equation 1 when: Step 3: Calculate for x = -1. y &= (1)/(2)x + 2 \\ y &= (1)/(2)(-1) + 2 \\ y &= -(1)/(2) + 2 \\ y &= -0.5 + 2 \\ y &= 1.5 Step 4: Calculate for x = 2. y &= (1)/(2)x + 2 \\ y &= (1)/(2)(2) + 2 \\ y &= 1 + 2 \\ y &= 3 Equation 2: y = 2x - 4 Step 5: Calculate output (y) values for Equation 2. • For x = -2: y = 2(-2) - 4 = -4 - 4 = -8 • For x = -1: y = 2(-1) - 4 = -2 - 4 = -6 • For x = 0: y = 2(0) - 4 = 0 - 4 = -4 • For x = 0.5: y = 2(0.5) - 4 = 1 - 4 = -3 • For x = 2: y = 2(2) - 4 = 4 - 4 = 0 Step 6: Complete the table for Equation 2. |c|c|c|c|c|c| Input (x) & -2 & -1 & 0 & 0.5 & 2 \\ Output (y) & -8 & -6 & -4 & -3 & 0 \\ Ordered Pair (x; y) & (-2; -8) & (-1; -6) & (0; -4) & (0.5; -3) & (2; 0) \\ What's next? Send 'em! 📸