\(\begin{array}{c|c} x & 0 & 2 & 4 & 6\\ \hline y & 1 & 2 & 3 & 4\end{array}\). The table is for the relation y = mx + c where m and c are constants. What is the equation of the line described in the tablet?
A. y = 2x B. y = x + 1 C. y = x D. y = \(\frac{1}{2}x + 1\)
Correct Answer: D
Explanation
y = mx + c; when x = 0; y = 1 1 = m(0) + c; 1 = 0 + c; c = 1 when x = 2; y = 2 2 = m(2) + c; 2 = 2m + c; but c = 1 2 = 2m + 1 2 - 1 = 2m 2m = 1 m = \(\frac{1}{2}\) y = \(\frac{1}{2}\)x + 1
