Linear Relationships 2 — Heart of Algebra

Questions in this quiz (8)

1. A line models the temperature (°F) over time (hours): $$T=68-3t$$ What does the slope represent?

   • The temperature decreases 3°F per hour
   • The temperature increases 3°F per hour
   • The temperature is 3°F at time 0
   • The temperature decreases by 68°F per hour

2. The line graphed in the $$xy$$-plane below models the total cost, in dollars, for a scooter rental, $$y$$, based on the number of minutes ridden, $$x$$.According to the graph, what is the cost for each additional minute of scooter use, in dollars?

   • $$0.20$$
   • $$0.25$$
   • $$0.35$$
   • $$0.5$$

3. A hiker begins climbing a mountain from a base camp that is $$120$$ meters above sea level. The hiker climbs at a constant rate of $$6$$ meters per minute. Which of the following equations gives the height $$H$$, in meters, of the hiker $$t$$ minutes after leaving the base camp?

   • $$H=6−120t$$
   • $$H = 6t + 120$$
   • $$H=120−6t$$
   • $$H=120t+6$$

4. What is the equation of the line that passes through the point $$(-3,2)$$ and is parallel to the graph of $$y=-4x+1$$ in the $$xy$$-plane?

   • $$y=-4x-3$$
   • $$y=-4x-10$$
   • $$y=4x+2$$
   • $$y=-4x+2$$

5. The function $$g(m)=18m+12$$ gives the estimated height, in centimeters, of a sunflower $$m$$ months after it was planted. Which of the following is the best interpretation of the number $$12$$ in this context?

   • The sunflower will grow for $$12$$ months.
   • The sunflower is expected to grow $$12$$ centimeters each month.
   • The maximum height of the sunflower will be $$12$$ centimeters.
   • The sunflower was estimated to be $$12$$ centimeters tall when it was planted.

6. The graph of the linear function $$y=g(x)$$ is shown. What is the $$y$$-intercept of the graph of $$y=g(x)$$?

   • $$(0,5)$$
   • $$(5,0)$$
   • $$(4,5)$$
   • $$(0,4)$$

7. What is the equation of the line shown in the $$xy$$–plane above?

   • $$y=-x+6$$
   • $$y=-\frac{3}{4}x+6$$
   • $$y=-\frac{7}{9}x+1$$
   • $$y=-7x+9$$

8. If two lines have the same $$y$$-intercept but different slopes, how many times will the lines intersect?

   • Never
   • Exactly once
   • Twice
   • Infinitely many times