Question

Use the table to write a linear function that relates y to x.



y=

Answer 1

A linear function that relates y to x is:

`y\:=\:(2)/(3)x\:+\:5`

The graph of the linear function is also attached.

Explanation:

Given the table

x -3 0 3 6

y 3 5 7 9

The slope-intercept form of the line equation

`y = mx+b`

where

• m is the slope

• b is the y-intercept

Taking two points (-3, 3) and (0, 5) from the table to determine the slope of the linear function

• (x₁, y₁) = (-3, 3)

• (x₂, y₂) = (0, 5)

Using the formula

Slope = m = [y₂ - y₁] / [x₂ - x₁]

= [5 - 3] / [0 - (-3)]

= 2 / 3

Thus, the slope of the line = m = 2/3

We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.

From the table, it is clear

at x = 0, y = 5

Thus, the y-intercept b = 5

substituting m = 2/3 and b = 5 in the slope-intercept form of the line equation

`y = mx+b`

`y\:=\:(2)/(3)x\:+\:5`

Therefore, a linear function that relates y to x is:

`y\:=\:(2)/(3)x\:+\:5`

The graph of the linear function is also attached.