Given:
Table of values.
To find:
The equation in point slope form.
Solution:
From the given table it is clear that, the relationship is linear because the rate of change is constant because if x-value increases by 2 then y-values increases by 16.
Consider any two points from the table, i.e., (2,16) and (4,32).
[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]Slope=\dfrac{32-16}{4-2}[/tex]
[tex]Slope=\dfrac{16}{2}[/tex]
[tex]Slope=8[/tex]
The point is (2,16) and the slope is 8, so the point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-16=8(x-2)[/tex]
Therefore, the relationship is linear and point slope form is [tex]y-16=8(x-2)[/tex].
