1. **Stating the problem:** We are given the linear equation $3X + 5Y = 120$ and asked to analyze it. 2. **Formula and rules:** This is a linear equation in two variables $X$ and $Y$. To graph it, find the intercepts by setting one variable to zero and solving for the other. 3. **Finding the X-intercept:** Set $Y=0$: $$3X + 5(0) = 120 \implies 3X = 120 \implies X = \frac{120}{3} = 40$$ So the X-intercept is $(40,0)$. 4. **Finding the Y-intercept:** Set $X=0$: $$3(0) + 5Y = 120 \implies 5Y = 120 \implies Y = \frac{120}{5} = 24$$ So the Y-intercept is $(0,24)$. 5. **Graph interpretation:** The line passes through $(40,0)$ and $(0,24)$, which matches the description. 6. **Summary:** The equation $3X + 5Y = 120$ represents a straight line with intercepts at $(40,0)$ and $(0,24)$. Final answer: The intercepts are $X=40$ and $Y=24$ and the line equation is $3X + 5Y = 120$.