Question

I need help on these two questions! I’ll give 20 points for it!

Answer 1

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:

$y=mx+q$

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:

$m=\frac{\Delta y}{\Delta x}$

Choosing (0,13) and (5,28) for the 2 points, we find:

$m=\frac{28-13}{5-0}=\frac{15}{5}=3$

So the slope is 3. Therefore, the equation of the line is

$y=3x+13$