Answer:
Option A is correct.
d = 50t shows the relationship between d and t
Step-by-step explanation:
Point slope form: For a point [tex](x_1, y_1)[/tex] and a slope m, the equation of the line can be written as
[tex]y-y_1=m(x-x_1)[/tex] ......[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) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{100-50}{2-1}=\frac{50}{1} =50[/tex]
⇒[tex]m= 50[/tex]
Now, by point slope intercept form:
Substitute m= 50 and (1, 50) in [1]
we have;
[tex]y -50 = 50(x-1)[/tex]
Using distributive property: [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]
y -50 = 50x -50
Add both sides 50 we get;
y -50+ 50= 50x -50 + 50
Simplify:
[tex]y =50x[/tex]
∵y = d represents the distance and x = t represents the time;
then, our equation become:
[tex]d = 50t[/tex]
