Question: Find the x and y intercepts
of this linear equation.
12x + 30y = 180
x-intercept ([ ? ], [ ])
y-intercept ([ ], [ ])
1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$12x + 30y = 180$$.
2. **Recall the intercept definitions:**
- The x-intercept is where the graph crosses the x-axis, so $$y=0$$.
- The y-intercept is where the graph crosses the y-axis, so $$x=0$$.
3. **Find the x-intercept:**
Set $$y=0$$ in the equation:
$$12x + 30(0) = 180$$
$$12x = 180$$
Divide both sides by 12:
$$\cancel{12}x = \frac{180}{\cancel{12}}$$
$$x = 15$$
So the x-intercept is $$(15, 0)$$.
4. **Find the y-intercept:**
Set $$x=0$$ in the equation:
$$12(0) + 30y = 180$$
$$30y = 180$$
Divide both sides by 30:
$$\cancel{30}y = \frac{180}{\cancel{30}}$$
$$y = 6$$
So the y-intercept is $$(0, 6)$$.
**Final answer:**
- x-intercept: $$(15, 0)$$
- y-intercept: $$(0, 6)$$