SAT Linear Equations in Two Variables Questions
Lines in the xy-plane. Slope, intercepts, and moving between an equation, a table and a graph without losing the thread.
In short
- Linear Equations in Two Variables is part of Algebra, about 35% of the scored Math questions: 13 to 15 on every test.
- Math questions from all four areas are mixed in each module and arranged from easiest to hardest.
- Slope/intercept swap is the trap Rivie's practice tests set most often in Linear Equations in Two Variables questions.
Common traps
Most common first, from Rivie's ten practice tests.
Slope/intercept swap
In y = mx + b, the slope is m and the y-intercept is b. The wrong choice picks whichever number stands alone (b) as the slope, or whichever has x next to it (m) as the intercept.
The usual mistake: You match by which number 'looks like' a slope (small, positive) without checking the structure. y = 7 + 2x has slope 2, not 7: the leading number isn't always the slope.
Slope formula substitution
Slope = (y₂ − y₁) / (x₂ − x₁). The wrong choice subtracts in inconsistent order: y₂ − y₁ on top, x₁ − x₂ on bottom, flipping the sign.
The usual mistake: You set up one direction in the numerator and reverse it in the denominator, often because you wrote the points in different orders. The fix is to label points 1 and 2 explicitly.
Try a question
From Rivie's practice tests. Pick an answer to see why it is right or wrong.
A line ℓ in the xy-plane is defined by 3x + 4y = 12. What is the x-intercept of line ℓ?
Video lessons
Free on YouTube, picked for this topic.