Question

The following points for a function are graphed in the coordinate plane: (0, 4), (1, 5), (2, 6), and (3, 7). What function is being graphed? y = x + 4 y = 4 x 3 x + 4 y = 2 x + 3

Answer 1

$\textbf{Given:}$  

$\textsf{Points are (0,4), (1,5), (2,6) and (3,7)}$

$\textbf{To find:}$  

$\textsf{The function satisfy by the given points}$

$\textbf{Solution:}$  

$\textsf{First we find out equation line passing through (0,4) and (1,5)}$  

$\mathsf{\dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}}$  

$\mathsf{\dfrac{y-4}{5-4}=\dfrac{x-0}{1-0}}$  

$\mathsf{\dfrac{y-4}{1}=\dfrac{x}{1}}$  

$\mathsf{y-4=x}$  

$\implies\boxed{\mathsf{y=x+4}}$  

$\mathsf{For\;x=2\;and\;y=6,}$  

$\mathsf{6=2+4}$  

$\mathsf{6=6}$  

$\mathsf{For\;x=3\;and\;y=7,}$  

$\mathsf{7=3+4}$  

$\mathsf{7=7}$  

$\textsf{y=x+4 is satisfied by the other two points}$  

$\textsf{Hence, the required graph is y=x+4}$