4. the graph below shows the number of blocks one person can walk over a period of time.
a. is the number of blocks this person walks proportional to time? how do you know?
b. what does the point (0,0) mean in the context of the situation?
c. what is the unit rate?
d. what point represents the unit rate on the graph?

Question

Accepted Answer

### Part a
# Explanation:
## Step1: Recall Proportionality Rule
For a relationship to be proportional, the graph must be a straight line passing through the origin $(0,0)$, and the ratio $\frac{y}{x}$ (where $y$ is number of blocks, $x$ is time) must be constant.
## Step2: Check the Graph
The graph is a straight line and passes through $(0,0)$. Let's check ratios: At $x = 5$, $y = 10$, ratio $\frac{10}{5}=2$. At $x = 10$, $y = 20$, ratio $\frac{20}{10}=2$. The ratio is constant.
# Answer:
Yes, the number of blocks is proportional to time. Because the graph is a straight line passing through the origin $(0,0)$ and the ratio of blocks to time (unit rate) is constant (e.g., $\frac{10}{5}=\frac{20}{10} = 2$).

### Part b
# Brief Explanations:
In the context of walking blocks over time, the point $(0,0)$ means when the time (in minutes) is $0$ (i.e., at the start, no time has passed), the number of blocks walked is also $0$. So at time $0$ minutes, the person has walked $0$ blocks.
# Answer:
The point $(0,0)$ means that when $0$ minutes have passed (at the start), the person has walked $0$ blocks.

### Part c
# Explanation:
## Step1: Define Unit Rate
Unit rate is the ratio of the number of blocks ($y$) to time ( $x$ ), i.e., $\text{Unit Rate}=\frac{\text{Number of Blocks}}{\text{Time}}$.
## Step2: Calculate Using Points
Take a point, e.g., $(5,10)$. Then $\text{Unit Rate}=\frac{10}{5}=2$ blocks per minute.
# Answer:
The unit rate is $2$ blocks per minute.

### Part d
# Explanation:
## Step1: Recall Unit Rate on Graph
The unit rate is represented by the point where $x = 1$ (since unit rate is per $1$ unit of $x$, here $x = 1$ minute). Using the unit rate of $2$ blocks per minute, when $x = 1$, $y=2$. But also, any point $(x,y)$ where $\frac{y}{x}=\text{unit rate}$ can represent it. From the graph, the point $(1,2)$ (or using the given points, like $(5,10)$ scaled down, but the standard unit rate point is $(1,2)$ as unit rate is per $1$ minute). Alternatively, since the unit rate is $2$ blocks per minute, the point $(1,2)$ represents the unit rate ( $1$ minute, $2$ blocks).
## Step2: Confirm with Given Points
We can also see that the point $(1,2)$ lies on the line (since the slope is $2$, equation $y = 2x$, so when $x = 1$, $y = 2$).
# Answer:
The point $(1,2)$ (or any point $(x,y)$ where $y = 2x$, like $(5,10)$ scaled to $x = 1$) represents the unit rate. Specifically, the point $(1,2)$ ( $1$ minute, $2$ blocks) shows the unit rate of $2$ blocks per minute.

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QUESTION IMAGE

Question

Explanation:

Part a

Step1: Recall Proportionality Rule

Step2: Check the Graph

Step1: Define Unit Rate

Step2: Calculate Using Points

Answer:

Part b