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:
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:
Choosing (0,13) and (5,28) for the 2 points, we find:
So the slope is 3. Therefore, the equation of the line is
one thing to bear in mind is that calculators have two modes, Degree mode and Radian mode, if your calculator is in Radian mode and you plug in tan(39), it thinks "tangent of 39 radians" and so it gives that, bearing in mind that 1 radian is about 57°.
So make if you're using degrees as the angle, make sure your calculator is in Degree mode first, thus tan(39) will mean "tangent of 39 degrees".