A food truck's daily cost is $y = 150 + 4x$ and its revenue is $y = 9x$, where $x$ is the number of meals sold. What does the intersection point of these two lines represent?

The maximum number of meals sold

The break-even point where cost equals revenue

The point where revenue exceeds cost by the most

The minimum number of meals needed to open

Plan A charges $y = 30 + 5x$ dollars and Plan B charges $y = 10 + 8x$ dollars, where $x$ is months. At the intersection point $(\,x, y\,) = (\,\ldots\,)$, what is true about the two plans?

Plan A is always cheaper than Plan B

Plan B is always cheaper than Plan A

Both plans cost exactly the same amount

The plans never cost the same amount

6-1 Graphing Systems of Equations Practice — Grade 9 math

6-1 Graphing Systems of Equations — Practice Questions

1. A food truck's daily cost is $y = 150 + 4x$ and its revenue is $y = 9x$, where $x$ is the number of meals sold. What does the intersection point of these two lines represent?
- A. The maximum number of meals sold
- B. The break-even point where cost equals revenue
- C. The point where revenue exceeds cost by the most
- D. The minimum number of meals needed to open
2. A company's cost equation is $y = 300 + 6x$ and its revenue equation is $y = 11x$, where $x$ is units sold. The break-even point occurs when $x = $ ___.
3. Car A's distance from a city is $y = 20 + 60x$ miles and Car B's is $y = 200 - 40x$ miles, where $x$ is hours. The two cars are at the same location when $x = $ ___ hours.
4. Plan A charges $y = 30 + 5x$ dollars and Plan B charges $y = 10 + 8x$ dollars, where $x$ is months. At the intersection point $(\,x, y\,) = (\,\ldots\,)$, what is true about the two plans?
- A. Plan A is always cheaper than Plan B
- B. Plan B is always cheaper than Plan A
- C. Both plans cost exactly the same amount
- D. The plans never cost the same amount
5. Gym A costs $y = 50 + 20x$ dollars and Gym B costs $y = 80 + 10x$ dollars per month, where $x$ is months. At the point of equal value, the total cost is $y = $ ___ dollars.
6. Which system of equations should be graphed to find the solution for the equation $3x - 1 = -2x + 4$?
- A. $y = 3x - 1$ and $y = -2x + 4$
- B. $y = 3x$ and $y = -2x$
- C. $y = 3x + 1$ and $y = -2x - 4$
- D. $y = 5x - 5$ and $y = 0$
7. To solve the equation $x^2 + 5 = 4x - 2$ by graphing, you would graph $y_1 = x^2 + 5$ and $y_2 = $ ___.
8. The graphs of $y = 4x - 7$ and $y = -x + 8$ intersect at the point $(3, 5)$. What is the solution to the equation $4x - 7 = -x + 8$?
- A. $x = 3$
- B. $x = 5$
- C. $x = 8$
- D. The solution cannot be determined.
9. To solve $|x + 4| = 2x - 1$ graphically, one equation to graph is $y = |x + 4|$. The other equation is $y = $ ___.
10. A student graphs the system $y = x^2 + 2x$ and $y = 3x + 6$ to find the solution to an equation. What was the original equation?
- A. $x^2 + 2x = 3x + 6$
- B. $x^2 - x - 6 = 0$
- C. $y = x^2 - x - 6$
- D. The original equation cannot be determined.