Question

this table show the total distance d, in miles, a car traveled after t hours.
which equation shows the relationship between d and t?
options:
○ d = 150t
○ d = t + 150
○ d = 50t
○ d = t + 50

table:
time in hours (t) | 0 | 1 | 2 | 3
distance in miles (d) | 0 | 50 | 100 | 150

Explanation:

Step1: Analyze the table data

From the table, when \( t = 0 \), \( d = 0 \); when \( t = 1 \), \( d = 50 \); when \( t = 2 \), \( d = 100 \); when \( t = 3 \), \( d = 150 \). We can see that the distance \( d \) is proportional to time \( t \), and the rate of change (slope) is \( \frac{50 - 0}{1 - 0}=50 \), \( \frac{100 - 50}{2 - 1} = 50 \), \( \frac{150 - 100}{3 - 2}=50 \). So the equation should be in the form \( d=kt \), where \( k = 50 \).

Step2: Check each option

• For \( d = 150t \): When \( t = 1 \), \( d=150\times1 = 150

eq50 \), so this is wrong.

• For \( d=t + 150 \): When \( t = 0 \), \( d = 150

eq0 \), so this is wrong.

• For \( d = 50t \): When \( t = 1 \), \( d = 50\times1=50 \); when \( t = 2 \), \( d = 50\times2 = 100 \); when \( t = 3 \), \( d = 50\times3=150 \), which matches the table.
• For \( d=t + 50 \): When \( t = 0 \), \( d = 50

eq0 \), so this is wrong.

Answer:

\( d = 50t \) (the option with \( d = 50t \))