Heart of Algebra: Linear Equations (2 variables) — Quiz 2

Questions in this quiz (10)

1. The equation $$3x+2y=20$$ represents a triangle where two sides each have length $$x$$ and the third side has length $$y$$. Which of the following is the best interpretation of $$20$$?

   • $$\text{The difference between the lengths of the sides}$$
   • $$\text{The sum of the lengths of the three sides}$$
   • $$\text{The length of one side}$$
   • $$\text{The average side length}$$

2. A line passes through the points $$(2,5)$$ and $$(8,17)$$. What is the slope of the line?

   • 2

3. A smoothie recipe uses $$3$$ cups of yogurt and $$2$$ bananas and contains $$780$$ milligrams of potassium. There are $$200$$ milligrams of potassium in $$1$$ cup of yogurt. How much potassium, in milligrams, is in $$1$$ banana?

   • $$90$$
   • $$100$$
   • $$120$$
   • $$180$$

4. The system $$4x+5y=1$$ $$ax+by=1$$ represents two perpendicular lines. Which of the following pairs of equations also represents perpendicular lines?

   • $$8x+5y=1\text{ and }ax-4y=1$$
   • $$8x+5y=1\text{ and }ax+4y=1$$
   • $$4x-5y=1\text{ and }ax+by=1$$
   • $$4x+5y=1\text{ and }2ax+by=1$$

5. The graph in the $$xy$$-plane models the possible combinations of length $$x$$, in meters, and width $$y$$, in meters, for a rectangle with a perimeter of $$36$$ meters. Which statement is the best interpretation of the point $$(8,10)$$ in this context?

   • $$\text{The length is }10\text{ m less than the perimeter, and the width is }8\text{ m less than the perimeter}$$
   • $$\text{The length is }10\text{ m, and the width is }8\text{ m}$$
   • $$\text{The length is }8\text{ m, and the width is }10\text{ m}$$
   • $$\text{The length is }8\text{ m less than the perimeter, and the width is }10\text{ m less than the perimeter}$$

6. Line $$k$$ is shown in the $$xy$$-plane. Line $$j$$ is perpendicular to line $$k$$. What is the slope of line $$j$$?

   • $$\frac{6}{5}$$

7. At a school fundraiser, tickets have different values depending on type. One student collected $$T$$ regular tickets and $$V$$ VIP tickets worth a total of $$980$$ points. The equation $$50T+70V=980$$ represents the situation. How many more points is a VIP ticket worth than a regular ticket?

   • $$20$$
   • $$50$$
   • $$70$$
   • $$120$$

8. A fruit stand sells small and large baskets of strawberries. The total sales were represented by the equation $$3.25x+5.75y=460$$, where $$x$$ is the number of small baskets sold and $$y$$ is the number of large baskets sold. What is the price, in dollars, of each small basket?

   • 3.25

9. What is the $$y$$-coordinate of the $$y$$-intercept of the graph of $$\frac{2x}{5}=-\frac{y}{4}+10$$ in the $$xy$$-plane?

   • 40

10. The graph of $$5x+4y=20$$ in the $$xy$$-plane has an $$x$$-intercept at $$(a,0)$$ and a $$y$$-intercept at $$(0,b)$$, where $$a$$ and $$b$$ are constants. What is the value of $$\frac{b}{a}$$?

    • $$\frac{4}{5}$$
    • $$\frac{5}{4}$$
    • $$-\frac{4}{5}$$
    • $$-\frac{5}{4}$$