Algebraic Reasoning 1A Practice Worksheet
Algebraic Reasoning
Unit 1A Extension & Mastery Practice
Name: Date:
Period: Score:
TEKS AR.2C Item 1
1. What is the equation in slope-intercept form of the line that passes through the four points given below?
\((-15, -7),\; (-5, 1),\; (0, 5),\; (10, 13)\)
Show work (slope & intercept calculations):
\(y =\)
\(x\; +\)
TEKS AR.2C Item 2
2. Use the table below to determine the linear function in slope-intercept form.
<table class="border-collapse border border-slate-300 text-center text-xs"><tbody><tr class="bg-slate-50"><td class="border border-slate-300 px-3 py-0.5 font-semibold text-slate-700 italic">\(x\)</td><td class="border border-slate-300 px-3.5 py-0.5">2</td><td class="border border-slate-300 px-3.5 py-0.5">5</td><td class="border border-slate-300 px-3.5 py-0.5">8</td><td class="border border-slate-300 px-3.5 py-0.5">11</td><td class="border border-slate-300 px-3.5 py-0.5">14</td></tr><tr><td class="border border-slate-300 px-3 py-0.5 font-semibold text-slate-700 italic">\(y\)</td><td class="border border-slate-300 px-3.5 py-0.5">8.3</td><td class="border border-slate-300 px-3.5 py-0.5">15.5</td><td class="border border-slate-300 px-3.5 py-0.5">22.7</td><td class="border border-slate-300 px-3.5 py-0.5">29.9</td><td class="border border-slate-300 px-3.5 py-0.5">37.1</td></tr></tbody></table>
Bank: 2.4 7.2 4.8 3.5 8.3
Step 1: Calculate slope \(\frac{\Delta y}{\Delta x}\):
Step 2: Calculate initial value (\(y\)-intercept):
\(y =\)
\(x\; +\)
TEKS AR.3A Item 3
3. Identify the key attributes (slope, \(y\)-intercept, and \(x\)-intercept) of the table below.
| \(x\) | \(f(x)\) |
|---|
| -9 | 72 |
| -3 | 48 |
| 3 | 24 |
| 9 | 0 |
| 15 | -24 |
Work space (calculate slope, evaluate \(x = 0\)):
Slope:
\(y\)-intercept: ( , )
\(x\)-intercept: ( , )
Algebraic Reasoning • Unit 1A Practice Page 1 of 2
Unit 1A Practice Continued Domain & Range (Items 4, 5A, 5B) • Function Rules (Item 6)
TEKS AR.7A Item 4
4. Choose the correct domain and range for the ray shown on the grid below.
x y -3 4
Choose the two that best apply:
Domain: \(x \ge -3\) Range: \(y \le 4\) Domain: \(x \le -3\) Range: \(y \ge 4\) Domain: \(x > -3\) Range: \(y < 4\)
TEKS AR.7A Item 5A
5A. Determine the domain and range based on the line segment with a positive slope shown on the grid below.
x y -7 5 -3 4
Show work (identify endpoints):
Domain:
Range:
TEKS AR.7A Item 5B
5B. Determine the domain and range based on the line segment with a negative slope shown on the grid below.
x y -5 6 4 -3
Show work (identify endpoints):
Domain:
Range:
TEKS AR.3E Item 6A
6A. Complete the table using the function rule:
\(K(x) = 2.25(20x)\)
<table class="border-collapse border border-slate-300 text-center text-[11px] w-full mb-1"><tbody><tr class="bg-slate-50"><td class="border border-slate-300 px-1 py-0.5 font-semibold text-slate-700 italic w-10">\(x\)</td><td class="border border-slate-300 px-1 py-0.5">2</td><td class="border border-slate-300 px-1 py-0.5">6</td><td class="border border-slate-300 px-1 py-0.5"><div class="w-7 h-4 border-b-2 border-slate-400 mx-auto"></div></td><td class="border border-slate-300 px-1 py-0.5"><div class="w-7 h-4 border-b-2 border-slate-400 mx-auto"></div></td></tr><tr><td class="border border-slate-300 px-1 py-0.5 font-semibold text-slate-700 italic w-10">\(K(x)\)</td><td class="border border-slate-300 px-1 py-0.5">90</td><td class="border border-slate-300 px-1 py-0.5"><div class="w-7 h-4 border-b-2 border-slate-400 mx-auto"></div></td><td class="border border-slate-300 px-1 py-0.5">360</td><td class="border border-slate-300 px-1 py-0.5">495</td></tr></tbody></table>
Work space (simplify & solve):
TEKS AR.3E Item 6B
6B. Complete the table using the function rule:
\(M(x) = 1.5(18x)\)
<table class="border-collapse border border-slate-300 text-center text-[11px] w-full mb-1"><tbody><tr class="bg-slate-50"><td class="border border-slate-300 px-1 py-0.5 font-semibold text-slate-700 italic w-10">\(x\)</td><td class="border border-slate-300 px-1 py-0.5"><div class="w-7 h-4 border-b-2 border-slate-400 mx-auto"></div></td><td class="border border-slate-300 px-1 py-0.5">8</td><td class="border border-slate-300 px-1 py-0.5 font-medium text-slate-600">3</td><td class="border border-slate-300 px-1 py-0.5"><div class="w-7 h-4 border-b-2 border-slate-400 mx-auto"></div></td></tr><tr><td class="border border-slate-300 px-1 py-0.5 font-semibold text-slate-700 italic w-10">\(M(x)\)</td><td class="border border-slate-300 px-1 py-0.5">270</td><td class="border border-slate-300 px-1 py-0.5"><div class="w-7 h-4 border-b-2 border-slate-400 mx-auto"></div></td><td class="border border-slate-300 px-1 py-0.5 font-medium text-slate-600">81</td><td class="border border-slate-300 px-1 py-0.5">324</td></tr></tbody></table>
Work space (simplify & solve):
Algebraic Reasoning • Unit 1A Practice Page 2 of 2
Unit 1A Extension Answer Key
Teacher Answer Key Algebraic Reasoning
Unit 1A Extension & Mastery Solutions
Full Worked Solutions TEKS AR.2C, AR.3A
TEKS AR.2C Item 1 Solution
1. Equation from four points: \((-15, -7),\; (-5, 1),\; (0, 5),\; (10, 13)\)
Step 1 (Slope): \(m = \frac{\Delta y}{\Delta x} = \frac{1 - (-7)}{-5 - (-15)} = \frac{8}{10} = \mathbf{0.8}\) (or \(\frac{4}{5}\)) Check: \(\frac{13 - 5}{10 - 0} = \frac{8}{10} = 0.8\) ✓
Step 2 (\(y\)-intercept): The table includes \((0, 5)\), where \(x = 0 \implies b = \mathbf{5}\).
Correct Equation: \(y = \mathbf{0.8}x + \mathbf{5}\) or \(y = \mathbf{\frac{4}{5}}x + \mathbf{5}\)
TEKS AR.2C Item 2 Solution
2. Linear function in slope-intercept form from table.
Step 1: Rate of Change (\(m\))
\(\Delta x = 5 - 2 = 3\)
\(\Delta y = 15.5 - 8.3 = 7.2\)
\(m = \frac{\Delta y}{\Delta x} = \frac{7.2}{3} = \mathbf{2.4}\)
Step 2: Initial Value (\(b\))
Backtrack 2 units to \(x = 0\):
\(b = 8.3 - 2(2.4) = 8.3 - 4.8\)
\(b = \mathbf{3.5}\)
Selected Bank values: 2.4 and 3.5 \(y = \mathbf{2.4}x + \mathbf{3.5}\)
TEKS AR.3A Item 3 Solution
3. Key attributes (slope, \(y\)-intercept, and \(x\)-intercept) of the table.
Slope (\(m\))
\(\Delta x = -3 - (-9) = 6\)
\(\Delta y = 48 - 72 = -24\)
\(m = \frac{-24}{6} = \mathbf{-4}\)
\(y\)-intercept (\(x = 0\))
Halfway between \(-3\) and \(3\):
\(f(0) = 24 - (-4)(3) = 36\)
\(y\)-int: \(\mathbf{(0, 36)}\)
\(x\)-intercept (\(y = 0\))
Found directly in table:
\(f(9) = 0\)
\(x\)-int: \(\mathbf{(9, 0)}\)
Slope: -4 \(y\)-intercept: (0, 36) \(x\)-intercept: (9, 0)
Algebraic Reasoning • Unit 1A Answer Key Page 1 of 2
Teacher Answer Key Unit 1A Continued
TEKS AR.7A • AR.3E Solutions
TEKS AR.7A Item 4 Solution (Ray)
Endpoint: Solid closed dot at \((-3, 4)\). Ray points downward and rightward.
Domain Analysis: Starts at \(x = -3\) and goes infinitely right: \(\mathbf{x \ge -3}\)
Range Analysis: Starts at maximum \(y = 4\) and goes infinitely down: \(\mathbf{y \le 4}\)
✓ Domain: \(\mathbf{x \ge -3}\)
✓ Range: \(\mathbf{y \le 4}\)
<table class="border-collapse border border-slate-300 text-center text-[10px] w-full mb-1"><tbody><tr class="bg-slate-100"><td class="border border-slate-300 px-1 py-0.5 font-bold italic w-10">\(x\)</td><td class="border border-slate-300 px-1 py-0.5">2</td><td class="border border-slate-300 px-1 py-0.5">6</td><td class="border border-slate-300 px-1 py-0.5 bg-emerald-100 font-bold text-emerald-900">8</td><td class="border border-slate-300 px-1 py-0.5 bg-emerald-100 font-bold text-emerald-900">11</td></tr><tr><td class="border border-slate-300 px-1 py-0.5 font-bold italic w-10">\(K(x)\)</td><td class="border border-slate-300 px-1 py-0.5">90</td><td class="border border-slate-300 px-1 py-0.5 bg-emerald-100 font-bold text-emerald-900">270</td><td class="border border-slate-300 px-1 py-0.5">360</td><td class="border border-slate-300 px-1 py-0.5">495</td></tr></tbody></table>
<table class="border-collapse border border-slate-300 text-center text-[10px] w-full mb-1"><tbody><tr class="bg-slate-100"><td class="border border-slate-300 px-1 py-0.5 font-bold italic w-10">\(x\)</td><td class="border border-slate-300 px-1 py-0.5 bg-emerald-100 font-bold text-emerald-900">10</td><td class="border border-slate-300 px-1 py-0.5">8</td><td class="border border-slate-300 px-1 py-0.5 font-medium">3</td><td class="border border-slate-300 px-1 py-0.5 bg-emerald-100 font-bold text-emerald-900">12</td></tr><tr><td class="border border-slate-300 px-1 py-0.5 font-bold italic w-10">\(M(x)\)</td><td class="border border-slate-300 px-1 py-0.5">270</td><td class="border border-slate-300 px-1 py-0.5 bg-emerald-100 font-bold text-emerald-900">216</td><td class="border border-slate-300 px-1 py-0.5 font-medium">81</td><td class="border border-slate-300 px-1 py-0.5">324</td></tr></tbody></table>
