Answer
b) $\dfrac{x}{6}-\dfrac{y}{8}=1$
Work Step by Step
a) Consider the equation of a line in general form:
$$Ax+By+C=0, A\not=0,B\not=0,C\not=0.\tag1$$
Calculate the $x$-intercept:
$$\begin{align*}
Ax+B(0)+C&=0\\
Ax&=-C\\
x&=-\dfrac{C}{A}.
\end{align*}$$
Calculate the $y$-intercept:
$$\begin{align*}
A(0)+By+C&=0\\
By&=-C\\
y&=-\dfrac{C}{B}.
\end{align*}$$
Because $C\not=0$ we can divide Eq. $(1)$ by $C$:
$$\dfrac{Ax}{C}+\dfrac{By}{C}+1=0.$$
Because $A\not=0,B\not=0$ we can rewrite the above equation:
$$\dfrac{x}{\dfrac{C}{A}}+\dfrac{y}{\dfrac{C}{B}}+1=0.$$
But $C/A=-a$ and $C/B=-b$, where $a$ and $b$ are the intercepts:
$$\begin{align*}
\dfrac{x}{-a}+\dfrac{y}{-b}&=-1\\
\dfrac{x}{a}+\dfrac{y}{b}&=1.\tag2
\end{align*}$$
b) We are given $a=6$ and $b=-8$. Use Eq. $(2)$ to write the two-intercept form of the equation:
$$\begin{align*}
\dfrac{x}{6}+\dfrac{y}{-8}&=1\\
\dfrac{x}{6}-\dfrac{y}{8}&=1.
\end{align*}$$
