Using point \((4, -5)\): \(y - (-5) = -2(x - 4) \implies \mathbf{y + 5 = -2(x - 4)}\).
• Common Misconceptions & Distractor Rationale:
Distractor A: Incorrect positive slope \(m = 2\) combined with point \((-2, 7)\).
Distractors C & D: Inverted slope \(m = -\frac{1}{2}\) caused by calculating \(\frac{\Delta x}{\Delta y}\).
Sign Error on Point Substitution: Writing \(y - 5\) instead of \(y - (-5) = y + 5\).
Unit 4 Assessment Answer Key • Blueprint Aligned Page 1 of 6
TEKS: A.12D, A.2F, A.2G
Page 2 of 6
4 A.12(D) • Supporting Drag & Drop
Tiles: \([-8]\) and \([42]\) • \(a_n = -8n + 42\)
• Step-by-Step Breakdown:
1. Find common difference (\(d\)): \(d = a_2 - a_1 = 26 - 34 = -8\). Verify: \(18 - 26 = -8\).
2. Substitute into explicit formula: \(a_n = a_1 + d(n - 1) = 34 + (-8)(n - 1)\).
3. Distribute & simplify: \(a_n = 34 - 8n + 8 \implies \mathbf{a_n = -8n + 42}\).
• Common Misconceptions & Tile Traps:
Tile 34 as Constant: Students write \(a_n = -8n + 34\), forgetting that \(a_1\) is the 1st term, not the 0th term (\(a_0 = 34 - (-8) = 42\)).
Tile 8 (Positive Difference): Students fail to notice the sequence is decreasing and select \(+8\) instead of \(-8\).
Tile -42: Sign error during distribution, subtracting 8 instead of adding 8 (\(34 - 8 = 26\)).
5 A.2(F) • Supporting Multiple Choice
Correct Option: A • \(y = \frac{1}{2}x - 3\)
• Step-by-Step Breakdown:
1. Identify original slope: Line \(p\) has slope \(m_1 = -2\).
2. Determine perpendicular slope (\(m_\perp\)): Take negative reciprocal: \(m_\perp = -\frac{1}{-2} = \frac{1}{2}\).
3. Substitute point \((8, 1)\) to solve for \(b\):
\(y = mx + b \implies 1 = \frac{1}{2}(8) + b \implies 1 = 4 + b \implies b = -3\).
4. Assemble equation: \(\mathbf{y = \frac{1}{2}x - 3}\).
• Common Misconceptions & Distractor Rationale:
Distractor C (\(y = -\frac{1}{2}x + 5\)): Took reciprocal but forgot to change the sign from negative to positive.
Distractor B (\(y = 2x - 15\)): Changed the sign but forgot to take the reciprocal of 2.
Distractor D (\(y = \frac{1}{2}x + 1\)): Substituted \(y\)-coordinate 1 directly as the \(y\)-intercept \(b\).
6 A.2(G) • Supporting Drag & Drop
Equation: \(y = 4\) • Slope: \(0\)
• Step-by-Step Breakdown:
1. Identify line orientation: The line is perfectly horizontal and intersects the \(y\)-axis at \((0, 4)\).
2. Equation form: Every point has \(y = 4\) regardless of \(x \implies \mathbf{y = 4}\).
3. Calculate slope: Slope \(m = \frac{\Delta y}{\Delta x} = \frac{4 - 4}{x_2 - x_1} = \frac{0}{\Delta x} = \mathbf{0}\).
• Common Misconceptions & Distractor Rationale:
Undefined Slope: Students confuse horizontal and vertical lines. Use mnemonic HOY (Horizontal • 0 slope • \(y = \#\)) vs VUX (Vertical • Undefined • \(x = \#\)).
Tile \(x = 4\): Students think because the line is parallel to the \(x\)-axis, the equation must contain \(x\).
Unit 4 Assessment Answer Key • Blueprint Aligned Page 2 of 6
TEKS: A.2E (HS Only), A.2C (HS Only), A.2C
Page 3 of 6
7 HS Only • A.2(E) Multiple Choice
Correct Option: A • \(y = -\frac{1}{3}x + 4\)
• Step-by-Step Breakdown:
1. Find slope of line \(k\): Points on line \(k\) are \((-3, 0)\) and \((0, -1)\). Slope \(m = \frac{-1 - 0}{0 - (-3)} = -\frac{1}{3}\).
2. Parallel line property: Parallel lines have identical slopes \(\implies m = -\frac{1}{3}\).
3. Substitute point \(P(3, 3)\): \(y - 3 = -\frac{1}{3}(x - 3) \implies y - 3 = -\frac{1}{3}x + 1 \implies \mathbf{y = -\frac{1}{3}x + 4}\).
• Common Misconceptions & Distractor Rationale:
Distractor B (\(y = 3x - 6\)): Used the perpendicular slope \(m = 3\) instead of parallel slope \(-\frac{1}{3}\).
Distractor C (\(y = -\frac{1}{3}x + 2\)): Distribution sign error: wrote \(-\frac{1}{3}(-3) = -1\), giving \(b = -1 + 3 = 2\).
Distractor D (\(y = \frac{1}{3}x + 2\)): Miscalculated slope from graph as positive \(\frac{1}{3}\).
8 HS Only • A.2(C) Multiple Choice
Correct Option: B • \(C = 48h + 65\)
• Step-by-Step Breakdown:
1. Identify constant rate of change (slope \(m\)): Labor cost is \(\$48\) per hour \(\implies 48h\).
2. Identify initial starting value (\(y\)-intercept \(b\)): Flat diagnostic fee is \(\$65\).
3. Write total cost function: \(\text{Total Cost} = \text{Rate} \times \text{Hours} + \text{Flat Fee} \implies \mathbf{C = 48h + 65}\).
• Common Misconceptions & Distractor Rationale:
Distractor A (\(C = 65h + 48\)): Inverted variables; attached the hourly rate to the flat fee.
Distractor C (\(C = 113h\)): Added flat fee and hourly rate together (\(65 + 48 = 113\)), applying it to every hour.
Distractor D (\(C = 48h - 65\)): Subtracted the flat fee instead of adding it.
9 A.2(C) • Readiness Inline Choice
Dropdowns: \([-500]\) and \([30,000]\) • \(y = -500x + 30000\)
• Step-by-Step Breakdown:
1. Identify \(y\)-intercept from graph: Starts at \((0, 30000) \implies b = 30,000\).
2. Use marked point to find rate: Point is \((20, 20000)\). \(m = \frac{20000 - 30000}{20 - 0} = \frac{-10000}{20} = \mathbf{-500}\).
3. Assemble equation: \(\mathbf{y = -500x + 30000}\).
• Common Misconceptions:
Positive Rate Choice (\(+500\)): Choosing \(+500\) implies loan debt is increasing each month rather than paying down.
Unit Scale Confusion: Treating 30k as 30 and 20 as 2, yielding \(m = -5\) instead of \(-500\).
Unit 4 Assessment Answer Key • Blueprint Aligned Page 3 of 6
TEKS: A.2C, A.12E
Page 4 of 6
10 A.2(C) • Readiness Multiple Choice
Correct Option: A • \(y = \frac{4}{3}x - 2\)
• Step-by-Step Breakdown:
1. Calculate slope from table points \((-6, -10)\) and \((3, 2)\):
\(m = \frac{2 - (-10)}{3 - (-6)} = \frac{12}{9} = \frac{4}{3}\).
2. Solve for \(y\)-intercept \(b\) using \((3, 2)\):
\(y = mx + b \implies 2 = \frac{4}{3}(3) + b \implies 2 = 4 + b \implies b = -2\).
3. Assemble equation: \(\mathbf{y = \frac{4}{3}x - 2}\).
• Common Misconceptions & Distractor Rationale:
Distractor B & D (\(\frac{3}{4}x\)): Inverted slope calculation \(\frac{\Delta x}{\Delta y} = \frac{9}{12} = \frac{3}{4}\).
Distractor C (\(y = \frac{4}{3}x + 7\)): Calculation error solving for \(b\), adding 4 to both sides instead of subtracting.
11 A.2(C) • Readiness Multiple Choice
Correct Option: A • \(y = 50x + 45\)
• Step-by-Step Breakdown:
1. Form coordinate points: \((4, 245)\) and \((7, 395)\).
2. Compute monthly tuition rate (slope): \(m = \frac{395 - 245}{7 - 4} = \frac{150}{3} = \$50/\text{month}\).
3. Solve for registration fee (\(y\)-intercept):
\(245 = 50(4) + b \implies 245 = 200 + b \implies b = \$45\).
4. Function rule: \(\mathbf{y = 50x + 45}\).
• Common Misconceptions & Distractor Rationale:
Distractor B (\(y = 45x + 50\)): Swapped the rate per month with the one-time registration fee.
Distractor C (\(y = 60x + 5\)): Direct division error (\(245 / 4 \approx 61\)), assuming proportional relationship without fixed fee.
12 A.12(E) • Supporting Multiple Choice
Correct Option: B • \(y = 3x - 7\)
• Step-by-Step Breakdown:
1. Given standard form: \(6x - 2y = 14\).
2. Isolate \(y\)-term (subtract \(6x\)): \(-2y = -6x + 14\).
3. Divide EVERY term by \(-2\): \(y = \frac{-6x}{-2} + \frac{14}{-2} \implies \mathbf{y = 3x - 7}\).
• Common Misconceptions & Distractor Rationale:
Distractor A (\(y = -3x + 7\)): Dividing by \(+2\) instead of \(-2\) on left side, producing opposite signs.
Distractor C (\(y = 3x + 14\)): Dividing only the \(x\)-term by \(-2\) and forgetting to divide the constant 14.
Sign Error on Constant: Forgetting that \(14 \div (-2) = -7\) (not \(+7\)).
Unit 4 Assessment Answer Key • Blueprint Aligned Page 4 of 6
TEKS: A.3C, A.3B (HS Only), A.2E
Page 5 of 6
13 A.3(C) • Readiness Graphing Item
\(x\)-int: \((2, 0)\) • \(y\)-int: \((0, -3)\)
• Step-by-Step Breakdown:
1. Calculate \(x\)-intercept (\(y = 0\)): \(3x - 2(0) = 6 \implies 3x = 6 \implies x = 2 \rightarrow \mathbf{(2, 0)}\).
2. Calculate \(y\)-intercept (\(x = 0\)): \(3(0) - 2y = 6 \implies -2y = 6 \implies y = -3 \rightarrow \mathbf{(0, -3)}\).
3. Plot points & graph: Plot points at \((2, 0)\) and \((0, -3)\). Connect with a straight line through the entire grid.
• Common Misconceptions:
Reversed Coordinates: Plotting \((0, 2)\) on the \(y\)-axis instead of \((2, 0)\) on the \(x\)-axis.
Sign Error on \(y\)-intercept: Forgetting the negative sign on \(-2y\), plotting \((0, 3)\) instead of \((0, -3)\).
14 HS Only • A.3(B) Multiple Choice
Correct Option: B • \(-6\)
• Step-by-Step Breakdown:
1. Select two data pairs: \((-2.5, 33)\) and \((1, 12)\).
2. Compute \(\Delta y\): \(12 - 33 = -21\).
3. Compute \(\Delta x\): \(1 - (-2.5) = 1 + 2.5 = 3.5\).
4. Calculate rate of change: \(m = \frac{\Delta y}{\Delta x} = \frac{-21}{3.5} = \mathbf{-6}\).
• Common Misconceptions & Distractor Rationale:
Distractor C (\(-\frac{1}{6}\)): Inverted slope formula (\(\frac{\Delta x}{\Delta y} = \frac{3.5}{-21} = -\frac{1}{6}\)).
Distractor D (\(24\)): Sign error on subtraction with negative \(x\): \(1 - 2.5 = -1.5\), getting positive rate.
15 A.2(E) • Supporting Multiple Choice
Correct Option: A • \(2x + 3y = 9\)
• Step-by-Step Breakdown:
1. Identify original slope: \(y = -\frac{2}{3}x + 4 \implies m = -\frac{2}{3}\).
2. Parallel lines share identical slopes: \(m_{\text{parallel}} = -\frac{2}{3}\).
3. Substitute point \((6, -1)\): \(y - (-1) = -\frac{2}{3}(x - 6) \implies y + 1 = -\frac{2}{3}x + 4 \implies y = -\frac{2}{3}x + 3\).
4. Convert to Standard Form (\(Ax + By = C\)): Multiply by 3: \(3y = -2x + 9 \implies \mathbf{2x + 3y = 9}\).
• Common Misconceptions & Distractor Rationale:
Distractor B (\(3x - 2y = 20\)): Used the perpendicular slope \(m = \frac{3}{2}\) instead of parallel slope.
Distractor C (\(2x + 3y = 15\)): Sign error during point-slope conversion, adding 1 instead of subtracting 1.
Unit 4 Assessment Answer Key • Blueprint Aligned Page 5 of 6
Scoring Guide Short Constructed Response
2-Point Item
Score 2 / 2 Points • Full Credit Exemplar Complete Mathematical Reasoning
“The slope of the original line \(y = -\frac{2}{3}x + 4\) is \(-\frac{2}{3}\). Because parallel lines run in the exact same direction and never intersect, they must have identical slopes. Therefore, the new line also has a slope of \(m = -\frac{2}{3}\). Substituting the given point \((6, -1)\) into slope-intercept form gives \(-1 = -\frac{2}{3}(6) + b\). Since \(-\frac{2}{3}(6) = -4\), we have \(-1 = -4 + b\), which means \(b = 3\). The slope-intercept equation is \(y = -\frac{2}{3}x + 3\). Multiplying everything by 3 gives \(3y = -2x + 9\), and adding \(2x\) yields the standard form equation \(2x + 3y = 9\) (Choice A in Item 15).”
STAAR Analytical Scoring Rubric:
Point 1: Conceptual Justification (1 pt)
Point 2: Procedural Work & Equation (1 pt)
Score 1 / 2 Points (Partial Credit Examples):
Case A: Student writes correct equation \(2x + 3y = 9\) and shows work, but gives no explanation of why the slopes are equal.
Case B: Student explains parallel slopes are \(-\frac{2}{3}\), but makes an arithmetic error finding \(b\) (e.g., writes \(b = -5\)).
Score 0 / 2 Points (No Credit):
Student claims parallel lines have opposite reciprocal slopes (\(\frac{3}{2}\)), uses perpendicular slope throughout, or provides only an answer letter (“Choice A”) with no supporting reasoning.
• Common Pitfalls on Short Constructed Responses in Aware / STAAR:
Students frequently lose the justification point by jumping straight to numbers without stating in words why they chose \(m = -\frac{2}{3}\). Instruct students to explicitly include the word “parallel” and state “parallel lines have the same slope” in their written sentence.
Unit 4 Assessment Answer Key • Blueprint Aligned Page 6 of 6
