Question

kelly is comparing two linear functions. • function g has a slope of \\(\frac{1}{3}\\) and passes through the point \\((0, -1)\\). • function h passes through the points \\((8, 3)\\) and \\((10, 4)\\). kelly says that the initial value of function g is greater than the initial value of function h. is kelly correct? use the drop - down menus to explain. click the arrows to choose an answer from each menu. function h has an initial value of choose... . the initial value of function g is choose... the initial value of function h. kelly is choose... .

Explanation:

Step1: Find slope of Function H

The slope $m$ between points $(x_1,y_1)$ and $(x_2,y_2)$ is $\frac{y_2-y_1}{x_2-x_1}$.
$m = \frac{4-3}{10-8} = \frac{1}{2}$

Step2: Find equation of Function H

Use point-slope form $y - y_1 = m(x - x_1)$ with $(8,3)$:
$y - 3 = \frac{1}{2}(x - 8)$
Simplify to slope-intercept $y=mx+b$:
$y = \frac{1}{2}x - 4 + 3$
$y = \frac{1}{2}x - 1$

Step3: Identify initial values

Initial value is $b$ (when $x=0$):

• Function G: Given point $(0,-1)$, so initial value is $-1$.
• Function H: From equation, $b=-1$, so initial value is $-1$.

Step4: Compare initial values

$-1 = -1$, so they are equal.

Answer:

Function H has an initial value of $\boldsymbol{-1}$. The initial value of function G is $\boldsymbol{equal to}$ the initial value of function H. Kelly is $\boldsymbol{incorrect}$.