Question

Which function has the greater rate of change?

Answer 1

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 = $\frac{5}{6}$ x + 10 ← is in slope- intercept form

with slope m = $\frac{5}{6}$

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 = $\frac{15.75-14.25}{1+1}$ = $\frac{1.5}{2}$ = 0.75 = $\frac{3}{4}$

To compare the 2 fractions we require them to have a common denominator.

$\frac{5}{6}$ = $\frac{10}{12}$ and $\frac{3}{4}$ = $\frac{9}{12}$

$\frac{10}{12}$ > $\frac{9}{12}$

Thus Function 1 has the greater rate of change