Question

Write an equation in the form y = ... suggested by the pattern in the table

Answer 1

`y=x+6`

Explanation:

We have that the equation in its slope and intercept form is the following

`\begin{gathered} y=mx+b \\ \text{where m is the slope and b is the y-intercept} \end{gathered}`

We calculate the slope with the following equation

`m=(y_2-y_1)/(x_2-x_1)`

The points are (5, 11) and (9, 15)

Replacing:

`m=(15-11)/(9-5)=(4)/(4)=1`

now, for b

x = 7

y = 13

m = 1

replacing:

`\begin{gathered} 13=1\cdot7+b \\ b=13-7 \\ b=6 \end{gathered}`

The equation is:

`y=x+6`