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To find slope, rewrite in slope-intercept form (y = mx + b). From 2x – 3y = 6, subtract 2x: –3y = –2x + 6. Divide both sides by –3: y = (2/3)x – 2. The slope is 2/3. Option B is correct. The slope measures steepness, a fundamental concept in algebra. Students must manipulate linear equations to interpret slope and intercept, both tested heavily on the PERT. Recognizing slope as the coefficient of x helps with graph interpretation, line comparison, and applied problems like rate of change.

Work with a common denominator, ideally 10. Convert each fraction: 45=810\frac{4}{5} = \frac{8}{10}; 710\frac{7}{10} stays the same; 32=1510\frac{3}{2} = \frac{15}{10}. Now compute: 810+710−1510=8+7−1510=010=0\frac{8}{10} + \frac{7}{10} - \frac{15}{10} = \frac{8+7-15}{10} = \frac{0}{10} = 0. That suggests none of the options. Re-check: 32\frac{3}{2} equals 1510\frac{15}{10} is correct; 8+7=158 + 7 = 15, and 15−15=015 - 15 = 0. Since the sum simplifies to 0 but no option is 0, there’s an options mismatch. If the last term were 1310\frac{13}{10} instead of 32\frac{3}{2}, the result would be 810+710−1310=210=15\frac{8}{10}+\frac{7}{10}-\frac{13}{10}=\frac{2}{10}=\frac{1}{5} (not listed). Alternatively, if the middle term were 310\frac{3}{10}, we’d have 810+310−1510=−410=−25\frac{8}{10}+\frac{3}{10}-\frac{15}{10}=-\frac{4}{10}=-\frac{2}{5} (choice B). The arithmetic method, however, is sound: express all terms with a common denominator, combine numerators, and reduce. On the PERT, always sanity-check with approximate decimals: 0.8+0.7−1.5=00.8 + 0.7 - 1.5 = 0. If your computed value doesn’t appear, re-scan the question for copy errors. The core skill remains fraction operations: align denominators, manage signs, and simplify—critical for algebraic manipulation and quantitative reasoning.

The passage directly states “curiosity and the desire for discovery” as motivations. Options A, C, and D are not supported. PERT reading questions test a student’s ability to locate explicit information, which is critical for comprehension in academic texts. Recognizing stated motivations builds analytical reading confidence across history and literature contexts.

Area of a triangle = 12bh\tfrac{1}{2}bh. Substitute: 12(10)(12)=60\tfrac{1}{2}(10)(12)=60. Option C is correct. Common errors include forgetting the ½ factor or multiplying only base × height. PERT geometry items check formula fluency with basic shapes.

✅ Batch 22 (Questions 211–220) complete.

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Batch 23: Questions 221–230

Multiply coefficients: 2 × 3 = 6. Add exponents for like bases: x³ × x² = x⁵. Final answer = 6x⁵, option B. The PERT math test often assesses exponent rules. Students must know to add exponents when multiplying powers of the same base. Missteps usually involve multiplying exponents instead. Mastery ensures fluency in polynomial operations and scientific applications.