Given:
The table of values.
To find:
The relationship between the two variables and find the equation.
Solution:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Using the lope formula, we get
[tex]\dfrac{6-1}{1-0}=5[/tex]
[tex]\dfrac{11-6}{2-1}=5[/tex]
[tex]\dfrac{16-11}{3-2}=5[/tex]
[tex]\dfrac{21-16}{4-3}=5[/tex]
[tex]\dfrac{26-21}{5-4}=5[/tex]
The slope is constant, i.e., 5. It means the relationship between the two variables x and y is linear with slope 5.
It means the value of y increases by 5 as the value of x increases by 1.
The equation of the line is:
[tex]y=mx+b[/tex] ...(i)
Where, m is the slope and b is the y-intercept.
A point of linear relationship is (0,1). It means the y-intercept is 1.
Putting [tex]m=5,b=1[/tex] in (i), we get
[tex]y=5x+1[/tex]
Therefore, the required equation is [tex]y=5x+1[/tex].
