Question

e table below for questions he below represents a linear fi -5 7 1 07 -5 1 hat is the rate of change for action

Answer 1

We can calculate the rate of change between two points (x1,y1) and (x2,y2) as:

$r=\frac{y_2-y_1}{x_2-x_1}$

As function is linear, the rate of change will be constant for all points.

We choose points (-5,7) and (-3,1) and calculate the rate of change:

$r=\frac{y_2-y_1}{x_2-x_1}=\frac{1-7}{-3-(-5)}=\frac{-6}{2}=-3$

Then, the rate of change has a value of -3.

Now, we have to find the initial value.

We interpret that the initial valule of a function is the value of y when x=0.

To find that, we need to use the equation of the line.

Knowing the slope (m=-3) and one of the points, like (-5,7), we can write the slope-point form of the equation:

$\begin{gathered} y-y_0=m(x-x_0) \\ y-7=-3(x-(-5)) \\ y=-3(x+5)-7 \end{gathered}$

We then can find y(0) replacing x with 0:

$\begin{gathered} y(0)=-3(0+5)+7 \\ y(0)=-3\cdot5+7 \\ y(0)=-15+7 \\ y(0)=-8 \end{gathered}$

The initial value y(0) is y=-8

Answer:

2) -3 [Option B]

3) -8 [Option A]