AlgebraVery hardConstant so that a line passes through an intersection
Algebra practice question
In the xy-plane, the lines x + y = 9 and x − y = 1 intersect at a point P. For what value of c does the line y = 2x + c pass through P?
Answer: -6
P is (5, 4), and 4 = 2(5) + c gives c = −6.
Common wrong answers
- If you answered 4
- 4 is the y-coordinate of P.
- If you answered 6
- 6 has the sign wrong.
- If you answered -1
- −1 swaps the coordinates of P to (4, 5), giving 5 = 8 + c.
More Algebra questions
- Very hard
For what value of c does the system 3x − 2y = 8 and 9x + cy = 5 have no solution? - Very hard
In the system 5x + 4y = 32 and 3x − 2y = 6, what is the value of 8x + 2y? - Very hard
The solution set of the inequality |ax − b| ≤ 6, where a and b are constants and a > 0, is 3 ≤ x ≤ 9. What is … - Very hard
The function f is linear, and for every value of x, f(x + 2) − f(x) = 6. If f(5) = 4, what is the value of f(0… - Very hard
In the system of equations 2x + 3y = 12 and 5x − 2y = k, where k is a constant, the solution (x, y) satisfies … - Very hard
In the xy-plane, the system of equations kx + 6y = 12 and 2x + (k − 1)y = 6, where k is a constant, has infini…
Not affiliated with the College Board. SAT is a trademark of the College Board.