Respuesta :
We can calculate the rate of change between two points (x1,y1) and (x2,y2) as:
[tex]r=\frac{y_2-y_1}{x_2-x_1}[/tex]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:
[tex]r=\frac{y_2-y_1}{x_2-x_1}=\frac{1-7}{-3-(-5)}=\frac{-6}{2}=-3[/tex]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:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-7=-3(x-(-5)) \\ y=-3(x+5)-7 \end{gathered}[/tex]We then can find y(0) replacing x with 0:
[tex]\begin{gathered} y(0)=-3(0+5)+7 \\ y(0)=-3\cdot5+7 \\ y(0)=-15+7 \\ y(0)=-8 \end{gathered}[/tex]The initial value y(0) is y=-8
Answer:
2) -3 [Option B]
3) -8 [Option A]
