Which of the following equations represent the linear relationship between time, t, and velocity, v, shown in the table below?
A. v = 32t
B. v = 32t + 120
C. v = 120t
D. v = 120t + 32
E. v = 120t + 120
Correct Answer: B
Explanation/Reference:
Explanation:
A linear relationship means the associated graph is a line. So, you can think of the ordered pairs (t, v) as points on the line. Since (0, 120), (1,1 52), and (2, 184) are points on the line, the slope of the line is (152 – 120) / (1 – 0) = 32. Therefore, v = 32t + b, where b is the y-intercept of the line. Since (0, 120) is a point on the line, 120 = 32 x0 + b, or b = 120. Thus, an equation for the line is v = 32t + 120.
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