Question

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

Answer 1

Answer:

A linear function that relates y to x is:

$y\:=\:\frac{2}{3}x\:+\:5$

The graph of the linear function is also attached.

Step-by-step 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

$y = mx+b$

$y\:=\:\frac{2}{3}x\:+\:5$

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

$y\:=\:\frac{2}{3}x\:+\:5$

The graph of the linear function is also attached.