Answer:
Function 1
Step-by-step explanation:
The rate of change is measured by the slope m
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{5}{6}[/tex] x + 10 ← is in slope- intercept form
with slope m = [tex]\frac{5}{6}[/tex]
Calculate the slope of Function 2 using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 14.25) and (x₂, y₂ ) = (1, 15.75) ← 2 ordered pairs from the table
m = [tex]\frac{15.75-14.25}{1+1}[/tex] = [tex]\frac{1.5}{2}[/tex] = 0.75 = [tex]\frac{3}{4}[/tex]
To compare the 2 fractions we require them to have a common denominator.
[tex]\frac{5}{6}[/tex] = [tex]\frac{10}{12}[/tex] and [tex]\frac{3}{4}[/tex] = [tex]\frac{9}{12}[/tex]
[tex]\frac{10}{12}[/tex] > [tex]\frac{9}{12}[/tex]
Thus Function 1 has the greater rate of change
