Question 1
In the xy-plane, a line with slope 3 passes through the point (-6, 9). What is the y-intercept of the line?
- A.
-27
- B.
-9
- C.
27
- D.
33
Answer: C. 27
Use y = mx + b: 9 = (3)(-6) + b, so 9 = -18 + b and b = 27.
SAT · Math · Algebra
Linear equations in two variables
Linear equations in two variables is part of Algebra in the SAT Math section. The questions below are written in the style of the real test, each with the answer and a worked explanation.
Question types you will see here include two-variable constraint model, intercepts from standard form, write an equation from a context and point on a line.
Common traps: swapping coefficient and variable; interpreting the intercept as a total; treating both items as the same price.
Sample questions
Question 2
A hardware store sells screws individually for $0.15 each and in boxes for $9 each. On Monday, the store's revenue from screws was $54, as modeled by 0.15s + 9b = 54. What does 9 represent in this equation?
- A.
The number of boxes of screws the store sold
- B.
The number of screws in each box
- C.
The price, in dollars, of one box of screws
- D.
The store's total revenue, in dollars, from boxes of screws
Answer: C. The price, in dollars, of one box of screws
In 0.15s + 9b = 54, b counts boxes, so the coefficient 9 is the price per box: 9b is dollars from boxes (C). A confuses the coefficient with the variable b; B confuses price with quantity per box, which the equation does not give; D describes the whole term 9b, not the coefficient 9.
- A.
Question 3
In the xy-plane, a line passes through the points (2, 7) and (5, 16). The point (8, p) also lies on the line. What is the value of p?
- A.
9
- B.
19
- C.
25
- D.
34
Answer: C. 25
The slope is (16 − 7)/(5 − 2) = 3. Moving from (5, 16) to x = 8 is 3 units, so p = 16 + 3(3) = 25. A inverts the slope (1/3); B adds the slope once rather than three times; D adds 3 × 6 to the y-value at x = 5, using the x-distance from x = 2 on the wrong starting point.
- A.
Question 4
An e-book store lets a member borrow standard e-books at $4 each and premium e-books at $7 each. A member spends exactly $60. If s is the number of standard e-books and p is the number of premium e-books, which equation represents this situation?
- A.
7s + 4p = 60
- B.
11(s + p) = 60
- C.
4s + 7p = 60
- D.
4s + 7p = 60s
Answer: C. 4s + 7p = 60
C is correct: Standard e-books cost 4s and premium cost 7p, and the sum is the total spent, 60. A swaps the two prices. B charges both kinds at the combined price. D multiplies the total by s.
- A.
Question 5
A glass bridge's panel positions satisfy the line 3x − 4y = 18. The point (k, 3) lies on this line. What is the value of k?
- A.
2
- B.
10
- C.
30
- D.
54
Answer: B. 10
Substitute y = 3: 3k − 12 = 18, so 3k = 30 and k = 10 (B). Choice A comes from the sign slip 3k + 12 = 18; C stops at 3k = 30 without dividing; D multiplies 18 by 3 instead of dividing 30 by 3.
- A.
Find your real gaps
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