Question

Two linear functions are shown.

Answer 1

Answer:

Function A has a greater initial value because the initial value for Function A is 6 and the initial vale for Function B is 3

Step-by-step explanation:

The data for Function A is presented here as follows;

$\begin{array}{cc}x&y\\-1&9\\0&6\\1&3\\2&0\end{array}$

The slope of the function, 'm', is given using any two points as follows;

m = (9 - 3)/((-1) - 1) = -3

The slope of the function = -3

The equation of function in point and slope form is given as follows;

y - 3 = -3·(x - 1)

The equation of Function A, is therefore, given as follows;

y = 3 - 3·x + 3 = 6 - 3·x

∴ y = 6 - 3·x

The equation of Function B is given as follows;

y = 6·x + 3

The initial value of a function is given by the y-intercept of the function, where the input variable (x-variable) is zero

The initial value, (y-intercept) of Function A, f(0) is therefore found as follows;

f(x) = y = 6 - 3·x

f(0) = 6 - 3×0 = 6

The initial value of Function A, f(0) = 6

Similarly, the initial value, (y-intercept) of Function B, f(0) is found as follows;

f(x) = y = 6·x + 3

f(0) = 6×0 + 3 = 3

The initial value of the Function B, f(0) = 3

Therefore, we have that Function A has a greater initial value than Function B