4. Area of the Triangle Formed

The area of the triangle formed by the graph of the equation $2x + 3y = 12$ with the x-axis and y-axis can be calculated using the formula for the area of a triangle:

$\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$

• The base of the triangle is the distance along the x-axis, which is 6 units (from $(6, 0)$ to $(0, 0)$).
• The height of the triangle is the distance along the y-axis, which is 4 units (from $(0, 4)$ to $(0, 0)$).

Thus, the area is:

$\text{Area} = \frac{1}{2} \times 6 \times 4 = 12 \text{ square units}$

Would you like more details or have any questions? Here are some related questions to consider:

1. How would the graph change if the equation were $2x + 3y = 6$ instead?
2. What happens to the area of the triangle if the coefficients of x and y in the equation change?
3. How would you find the area if the equation was quadratic instead of linear?
4. Can you find the coordinates of another point on the line, not on the axes?
5. How can you verify that the area calculated geometrically matches algebraic methods?

Tip: Understanding the impact of coefficients in linear equations on the graph's slope can help predict changes in intersections with the axes.