Question

write the piecewise equations for the given graphs.
17.

Explanation:

Step1: Identify first segment domain

The first line segment spans $x=0$ to $x=3$.

Step2: Find first segment equation

Use points $(0,1)$ and $(3,-5)$. Slope: $m=\frac{-5-1}{3-0}=-2$. Y-intercept $b=1$. Equation: $y=-2x+1$ for $0\leq x\leq3$.

Step3: Identify second segment domain

The second line segment spans $x=4$ to $x=8$.

Step4: Find second segment equation

Use points $(4,-1)$ and $(8,0)$. Slope: $m=\frac{0-(-1)}{8-4}=\frac{1}{4}$. Substitute $(8,0)$: $0=\frac{1}{4}(8)+b \implies b=-2$. Equation: $y=\frac{1}{4}x-2$ for $4\leq x\leq8$.

Answer:

$$ y=
LATEXBLOCK0
$$