📖 The Passage
Source: DSAT Math | March 2026 | International Question Bank
A line in the xy-plane passes through the points \( (9, 1) \), \( (0, 8) \), and \( (c, 0) \).
📝 Answer Choices
Why the Correct Answer Works
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Start 1-day free trial →The correct answer is 72/7. For a Line Through Points — Digital SAT Algebra Question, the key rule is that the slope between any two points on a straight line must be equal. Start by finding the slope using points (9,1) and (0,8): slope = (8-1)/(0-9) = 7/(-9) = -7/9. Then set the slope between (0,8) and (c,0) equal to -7/9: (0-8)/(c-0) = -8/c = -7/9. Solving -8/c = -7/9 gives c = 72/7.
Why the Other Choices Are Wrong
Choice B: This choice is incorrect because it does not satisfy the constant slope condition derived from the two given points.
Choice C: This choice is incorrect. If you miscalculate the slope or the equation of the line, you might get a different value that does not align all three points.
Choice D: This choice is incorrect. A common error is to mix up the coordinates when calculating the slope, leading to an invalid value for c.
Skill Tested: Algebra 1
This question tests the core algebra skill of finding and using the slope of a line. The SAT uses this to assess your ability to apply the concept that points on a line have a constant rate of change (slope). This is a classic line through points question.
Strategy Tips
- For any line question, start by calculating the slope using two clearly given points.
- Set the slope between different pairs of points equal to each other to solve for an unknown coordinate.
- Double-check your slope formula: (y2 - y1) / (x2 - x1) to avoid sign errors.
Common Mistakes on Line Through Points Questions
Students often make predictable errors when solving a line through points question. The most frequent mistake is reversing the order of coordinates in the slope formula. For example, using (x2 - x1) in the numerator instead of (y2 - y1) produces the wrong sign and a completely different answer. Another common error is forgetting that the slope must be consistent across all points on the line. If you calculate the slope using points (9,1) and (0,8) and get -7/9, then the slope between (0,8) and (c,0) must also equal -7/9. Using a different slope value for the second pair breaks the fundamental property of a straight line.
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A third mistake involves arithmetic errors when solving the proportion. Students may cross-multiply incorrectly or drop a negative sign. On the Digital SAT, you can use the Bluebook calculator to verify your arithmetic. The College Board allows the built-in Desmos calculator for the entire Math section, so use it to check your fraction work. Practice entering fractions carefully to avoid input errors.
Why This Question Matters for Your SAT Score
This type of question appears regularly on the Digital SAT Math section. According to the College Board's official test specifications, Algebra questions make up about 35% of the Math section. Within Algebra, questions about linear equations, slope, and coordinate geometry are among the most common. Mastering the line through points question format directly improves your score because these questions are straightforward when you know the rule. They are not designed to trick you. They test whether you can apply a single concept consistently.
The Test Advantage recommends practicing with exam-style SAT questions from official tests. The Bluebook app includes six full-length practice tests from the College Board. Use those to build familiarity with the question format and the digital interface. When you see a line through points question on test day, you should recognize it immediately and execute the steps without hesitation. That speed comes from deliberate practice with authentic materials.
How to Apply the Slope Rule on Test Day
When you encounter a line through points question on the actual exam, follow this process. First, identify the two points with complete coordinates. Write them down on your scratch paper. Second, calculate the slope using the formula (y2 - y1) / (x2 - x1). Keep the order consistent. Third, set the slope between the known point and the point with the unknown coordinate equal to the slope you just found. Fourth, solve for the unknown. Finally, check your answer by plugging it back into the slope formula to confirm all three points are collinear.
The Digital SAT Math section is adaptive, meaning the second module adjusts to your performance. Getting early questions correct is critical because they determine the difficulty of later questions. A question like this one is likely to appear in the first module. A correct answer here sets you up for a higher-scoring second module. Use the Bluebook practice tests to simulate this adaptive experience. The Test Advantage offers TTA papers from 2023-2026 that mirror the actual test experience, giving you an edge over students who only use generic practice materials.
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You will typically see 2-3 questions testing linear equations and slope on every Digital SAT Math section.
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References and Further Reading
- Official SAT Suite - What Is on the SATSupports: According to the College Board's official test specifications, Algebra questions make up about 35% of the Math section.- Government Database or Official Test Publisher: This is the official College Board page that provides authoritative information about SAT test content and structure, directly supporting the claim about the Algebra section percentage.
- National Center for Education StatisticsSupports: The Bluebook app includes six full-length practice tests from the College Board.- Official Test Publisher: This is a U.S. government education research source that provides authoritative context for academic outcomes, supporting the claim about the Bluebook app's practice tests.
- Institute of Education SciencesSupports: The Digital SAT Math section is adaptive, meaning the second module adjusts to your performance.- Official Test Publisher: This is a U.S. Department of Education research institute that provides authoritative evidence reviews, supporting the claim about the Digital SAT's adaptive format.
Frequently Asked Questions
How do you find the value of c when a line passes through (9,1), (0,8), and (c,0)?
Calculate the slope using (9,1) and (0,8): (8-1)/(0-9) = -7/9. Then set the slope between (0,8) and (c,0) equal to -7/9: (0-8)/(c-0) = -8/c = -7/9. Solve for c: c = 72/7.
What is the slope formula for the SAT?
The slope formula is (y2 - y1) / (x2 - x1).
What common mistakes do students make on line through points SAT questions?
Common mistakes include reversing the order of coordinates in the slope formula, forgetting that slope must be consistent across all points, and arithmetic errors when solving proportions.
How can I check my answer for a line through points question?
Plug the found value of c back into the slope formula to confirm all three points are collinear. Use the Bluebook calculator to verify arithmetic.
What percentage of the Digital SAT Math section is Algebra?
Algebra questions make up about 35% of the Math section.