Answer:
Option A is correct.
d = 50t shows the relationship between d and t
Step-by-step explanation:
Point slope form: For a point
and a slope m, the equation of the line can be written as
......[1], where m is the slope of the line.
Here, d represents the total distance ( in miles) and t represents the time (in hours).
From the given table:
Consider any two points (1, 50) and (2, 100).
Calculate slope:
Slope(m) =
=
⇒![m= 50](https://tex.z-dn.net/?f=m%3D%2050)
Now, by point slope intercept form:
Substitute m= 50 and (1, 50) in [1]
we have;
![y -50 = 50(x-1)](https://tex.z-dn.net/?f=y%20-50%20%3D%2050%28x-1%29)
Using distributive property: ![a\cdot(b+c) = a\cdot b+ a\cdot c](https://tex.z-dn.net/?f=a%5Ccdot%28b%2Bc%29%20%3D%20a%5Ccdot%20b%2B%20a%5Ccdot%20c)
y -50 = 50x -50
Add both sides 50 we get;
y -50+ 50= 50x -50 + 50
Simplify:
![y =50x](https://tex.z-dn.net/?f=y%20%3D50x)
∵y = d represents the distance and x = t represents the time;
then, our equation become:
![d = 50t](https://tex.z-dn.net/?f=d%20%3D%2050t)