Question

Determine a relationship between the x- and y-values. Write an equation. Х 1 2 3 4 5 y 2 58 11 14

Answer 1

First, you can graph the pairs (x, y) and see what relationship they form

As you can see, they form a line. To find the equation of the line you can first obtain the slope using this formula

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \text{If you take } \\ (x_(1,)y_1)=(3,8) \\ (x_2,y_2)=(1,2) \\ \text{You have} \\ m=\frac{8-2_{}}{3-1} \\ m=(6)/(2)=3 \end{gathered}`

Finally, using the point slope equation you have

`\begin{gathered} y-y_1=m(x-x_1) \\ y-2=3(x-1) \\ y-2=3x-3 \\ y-2+2=3x-3+2 \\ y=3x-1 \end{gathered}`

Therefore, the equation that determines the relationship between the given values of x and y is y=3x-1.