1. The problem is to understand the equation of a plane or line in three variables: $3x - 8y - 7z = 58$. 2. This is a linear equation in the variables $x$, $y$, and $z$. It represents a plane in three-dimensional space. 3. To analyze or graph this plane, you can rearrange for one variable or find intercepts. For example, solving for $z$: $$3x - 8y - 7z = 58 \ -7z = 58 - 3x + 8y \ z = \frac{3x - 8y - 58}{7}$$ 4. The $x$-intercept occurs when $y=0$ and $z=0$: $$3x - 8(0) - 7(0) = 58 \ 3x = 58 \ x = \frac{58}{3}$$ 5. The $y$-intercept occurs when $x=0$ and $z=0$: $$3(0) - 8y - 7(0) = 58 \ -8y = 58 \ y = -\frac{58}{8} = -\frac{29}{4}$$ 6. The $z$-intercept occurs when $x=0$ and $y=0$: $$3(0) - 8(0) - 7z = 58 \ -7z = 58 \ z = -\frac{58}{7}$$ 7. Thus, the plane crosses the axes at $\left(\frac{58}{3}, 0, 0\right)$, $\left(0, -\frac{29}{4}, 0\right)$, and $\left(0, 0, -\frac{58}{7}\right)$. These points help visualize or graph the plane. 8. The final answer is the equation of the plane $3x - 8y - 7z = 58$ with intercepts as found.