Answer:
yes to both
Step-by-step explanation:
For a relationship to be a function then each value of x must relate to exactly one unique value of y.
This is the case in this table as
2 → 76
4 → 152
6 → 228
All unique values thus a function
To determine if it is linear then the rate of change is constant for each set of ordered pairs. This is measured using the slope formula.
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 76) and (x₂, y₂ ) = (4, 152 ) ← ordered pair from table
m = [tex]\frac{152-76}{4-2}[/tex] = [tex]\frac{76}{2}[/tex] = 38
Repeat with (x₁, y₁ ) = (4, 152) and (x₂, y₂ ) = (6, 228)
m = [tex]\frac{228-152}{6-4}[/tex] = [tex]\frac{76}{2}[/tex] = 38
Since rate of change is constant then function is linear
