Answer to Question #106022 in Algebra for Annisha

Question

Linear patterns of 33and 47

Answer 1

To determine a linear pattern, we need to know more than just one point like (33,47). However, if the table looks like this:

$$\begin{vmatrix} x&y\\ 3 & 4 \\ 3 & 7 \end{vmatrix},$$

then we can find the equation of the dependence of x upon y assuming linear pattern:

$$\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1},\\ \space\\ \frac{y-4}{7-4}=\frac{x-3}{3-3},\\$$

therefore, the equation cannot be found. However, the "pattern" may simply look like a line with x=3 for $4\leq y\leq7$: