1. **State the problem:** We are given the linear equation $30x + 6y = 60$ and want to analyze it, including finding intercepts. 2. **Formula and rules:** To find the x-intercept, set $y=0$ and solve for $x$. To find the y-intercept, set $x=0$ and solve for $y$. 3. **Find x-intercept:** Set $y=0$ in the equation: $$30x + 6\cancel{(0)} = 60 \implies 30x = 60$$ Divide both sides by 30: $$\cancel{30}x = \frac{60}{\cancel{30}} \implies x = 2$$ 4. **Find y-intercept:** Set $x=0$ in the equation: $$30\cancel{(0)} + 6y = 60 \implies 6y = 60$$ Divide both sides by 6: $$\cancel{6}y = \frac{60}{\cancel{6}} \implies y = 10$$ 5. **Interpretation:** The line crosses the x-axis at $(2,0)$ and the y-axis at $(0,10)$. This means if you have 2 quarters and 0 nickels, the total value is 60 cents, and if you have 0 quarters and 10 nickels, the total is also 60 cents. 6. **Rewrite equation in slope-intercept form:** Solve for $y$: $$30x + 6y = 60 \implies 6y = 60 - 30x$$ Divide both sides by 6: $$\cancel{6}y = \frac{60 - 30x}{\cancel{6}} \implies y = 10 - 5x$$ This shows the slope is $-5$ and the y-intercept is 10. **Final answer:** The x-intercept is $2$, the y-intercept is $10$, and the equation in slope-intercept form is $y = 10 - 5x$.