Question

The table show the total distance d, in miles, a car traveled after t hours. Time in hours (h) Distance in miles (d) 0 0 1 50 2 100 3 150 Which equation shows the relationship between d and t? d=50t d=t+150 d=150t d=t+50

Answer 1

Answer:

Option A is correct.

d = 50t shows the relationship between d and t

Step-by-step explanation:

Point slope form: For a point $(x_1, y_1)$ and a slope m, the equation of the line can be written as

$y-y_1=m(x-x_1)$ ......[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) =  $\frac{y_2-y_1}{x_2-x_1}$

               = $\frac{100-50}{2-1}=\frac{50}{1} =50$

⇒$m= 50$

Now, by point slope intercept form:

Substitute  m= 50 and (1, 50) in [1]

we have;

$y -50 = 50(x-1)$

Using distributive property: $a\cdot(b+c) = a\cdot b+ a\cdot c$

y -50 = 50x -50

Add both sides 50 we get;

y -50+ 50= 50x -50 + 50

Simplify:

$y =50x$

∵y = d represents the distance and x = t represents the time;

then, our equation become:

$d = 50t$

Answer 2

Answer:

A. d=50t

Step-by-step explanation:

I took the test online in K12 and when I reviewed it said that A. d=50t is the correct answer.