a) See below
b) y = 3x + 13
Step-by-step explanation:
a)
An example of story that is represented by the graph is the following:
Micheal is initially at a distance of 13 m from his house. Then, he walks at a speed of 3 meters per second away from the house, and after 5 seconds, he is at 28 m from the house.
Explanation:
In the graph, we have represented:
- Micheal's position along the y-axis
- The time along the x-axis
As we can see, when x = 0 (time = 0), Micheal's position is y = 13 m (here the origin refers to the position of the house). Then, the slope of the line is 3 m/s, which corresponds to Micheal's velocity (in a position-time graph, the slope is equal to the velocity).
b)
We want to find the equation that describes this graph.
The equation of a line can be written in the following form:
[tex]y=mx+q[/tex]
where
m is the slope
q is the y-intercept
The y-intercept is the value of y when x = 0: from the table, we see that when x = 0, then y = 13, so this is the y-intercept:
q = 13
The slope can be found by taking 2 points along the line and calculating the ratio between the change in the y-value and the change in the x-value:
[tex]m=\frac{\Delta y}{\Delta x}[/tex]
Choosing (0,13) and (5,28) for the 2 points, we find:
[tex]m=\frac{28-13}{5-0}=\frac{15}{5}=3[/tex]
So the slope is 3. Therefore, the equation of the line is
[tex]y=3x+13[/tex]
