Question

introduction to slope - item 32604
use the two graphs to help complete the statements below.
graph a (shows a graph with lawns mowed on y - axis and time (days) on x - axis, a line from (0,0) to some point)
graph b (shows a graph with lawns mowed on y - axis and time (days) on x - axis, a line from (0,0) to some point)
graph a:
unit rate = \\(\frac{\text{change in lawns mowed}}{\text{change in time}}\\) = \\(\square\\) lawns per day
graph b:
slope = \\(\frac{\text{change in } y}{\text{change in } x}\\) = \\(\square\\)

Explanation:

Step1: Analyze Graph A

To find the unit rate (slope) for Graph A, we use two points on the line. Let's take (0, 0) and (5, 25) (assuming the grid has time on the x - axis and lawns mowed on the y - axis). The change in lawns mowed ($\Delta y$) is $25 - 0=25$, and the change in time ($\Delta x$) is $5 - 0 = 5$. The unit rate is $\frac{\Delta y}{\Delta x}=\frac{25}{5}=5$ lawns per day.

Step2: Analyze Graph B

For Graph B, let's take two points, say (0, 0) and (5, 15). The change in lawns mowed ($\Delta y$) is $15 - 0 = 15$, and the change in time ($\Delta x$) is $5 - 0=5$. The slope (change in y over change in x) is $\frac{15}{5}=3$.

Answer:

For Graph A: 5
For Graph B: 3