1. The problem is to solve a linear equation using the intercept method. 2. The intercept method involves finding where the line crosses the axes. 3. Suppose the equation is $ax + by = c$. 4. To find the x-intercept, set $y=0$ and solve for $x$: $$ax + b\cancel{0} = c \implies x = \frac{c}{a}$$ 5. To find the y-intercept, set $x=0$ and solve for $y$: $$a\cancel{0} + by = c \implies y = \frac{c}{b}$$ 6. These intercepts give points $(\frac{c}{a}, 0)$ and $(0, \frac{c}{b})$ which can be used to graph or understand the line. 7. This method is useful for quickly sketching or solving linear equations.