Heart of Algebra: Linear Equations (2 variables) — Quiz 1

Questions in this quiz (10)

1. Which equation best represents the line shown in the graph?

   • y=-x-8

2. A line in the $$xy$$-plane has a slope of $$\frac{3}{4}$$ and passes through the point $$(0,-2)$$. Which equation represents this line?

   • $$y=\frac{3}{4}x-2$$
   • $$y=-\frac{3}{4}x-2$$
   • $$y=\frac{4}{3}x-2$$
   • $$y=\frac{3}{4}x+2$$

3. Line $$k$$ is defined by $$y=-5x+7$$. Line $$j$$ is parallel to line $$k$$ in the $$xy$$-plane. What is the slope of line $$j$$?

   • $$-5$$
   • $$5$$
   • $$\frac{1}{5}$$
   • $$-\frac{1}{5}$$

4. On a $$180$$-mile trip, Sofia drove at an average speed of $$60$$ miles per hour for the first $$x$$ hours. She then completed the trip at an average speed of $$40$$ miles per hour for the remaining $$y$$ hours. If $$x=2$$, what is the value of $$y$$?

   • 3/2

5. Line $$p$$ is defined by $$4y-8x=16$$. Line $$r$$ is perpendicular to line $$p$$. What is the slope of line $$r$$?

   • $$\frac{1}{2}$$
   • $$-\frac{1}{2}$$
   • $$2$$
   • $$-2$$

6. Line $$\ell$$ is defined by $$2x+5y=10$$. Line $$n$$ is perpendicular to line $$\ell$$. What is the slope of line $$n$$?

   • 5/2

7. When a line is graphed in the $$xy$$-plane, it has an $$x$$-intercept of $$(3,0)$$ and a $$y$$-intercept of $$(0,-6)$$. What is the slope of the line?

   • $$-2$$
   • $$2$$
   • $$-\frac{1}{2}$$
   • $$\frac{1}{2}$$

8. A school has a $$3$$-acre field and a $$12$$-acre forest. The total number of trees is $$2,100$$. The equation $$3x+12y=2100$$ represents this situation. Which is the best interpretation of $$y$$?

   • $$\text{The total number of trees in the forest}$$
   • $$\text{The number of acres in the forest}$$
   • $$\text{The average number of trees per acre in the forest}$$
   • $$\text{The average number of trees per acre in the field}$$

9. Lena made $$40$$ cups of lemonade. She poured the lemonade into $$x$$ small cups and $$y$$ large cups. The equation $$2x+5y=40$$ represents this situation. Which is the best interpretation of $$2x$$?

   • $$\text{The number of small cups used}$$
   • $$\text{The number of large cups used}$$
   • $$\text{The total number of cups in the small cups}$$
   • $$\text{The total number of cups in the large cups}$$

10. The table shows two points on a line. The $$y$$-intercept of the line is $$(0,b)$$. What is the value of $$b$$?

    • 18