Answer:
A linear function that relates y to x is:
[tex]y\:=\:\frac{2}{3}x\:+\:5[/tex]
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
[tex]y = mx+b[/tex]
where
Taking two points (-3, 3) and (0, 5) from the table to determine the slope of the linear function
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
[tex]y = mx+b[/tex]
[tex]y\:=\:\frac{2}{3}x\:+\:5[/tex]
Therefore, a linear function that relates y to x is:
[tex]y\:=\:\frac{2}{3}x\:+\:5[/tex]
The graph of the linear function is also attached.
