Triangle formed by the lines y = 0, 4x + 3y = 12 and 4x – 3y = – 12 is

To find the triangle formed by the lines y = 0, 4x + 3y = 12, and 4x – 3y = –12, we need to follow these steps:

Step 1: Find the x-intercepts of the lines y = 0, 4x + 3y = 12, and 4x – 3y = –12.

• For the line y = 0, the x-intercept is when y = 0, so x = 0. Therefore, the x-intercept is (0, 0).
• For the line 4x + 3y = 12, we can find the x-intercept by setting y = 0 and solving for x. So, 4x + 3(0) = 12, which simplifies to 4x = 12. Dividing both sides by 4, we get x = 3. Therefore, the x-intercept is (3, 0).
• For the line 4x – 3y = –12, we can find the x-intercept by setting y = 0 and solving for x. So, 4x – 3(0) = –12, which simplifies to 4x = –12. Dividing both sides by 4, we get x = –3. Therefore, the x-intercept is (-3, 0).

Step 2: Find the y-intercepts of the lines y = 0, 4x + 3y = 12, and 4x – 3y = –12.

• For the line y = 0, the y-intercept is when x = 0, so y = 0. Therefore, the y-intercept is (0, 0).
• For the line 4x + 3y = 12, we can find the y-intercept by setting x = 0 and solving for y. So, 4(0) + 3y = 12, which simplifies to 3y = 12. Dividing both sides by 3, we get y = 4. Therefore, the y-intercept is (0, 4).
• For the line 4x – 3y = –12, we can find the y-intercept by setting x = 0 and solving for y. So, 4(0) – 3y = –12, which simplifies to -3y = –12. Dividing both sides by -3, we get y = 4. Therefore, the y-intercept is (0, 4).

Step 3: Plot the x-intercepts and y-intercepts on a coordinate plane.

Step 4: Connect the points (0, 0), (3, 0), and (-3, 0) to form the triangle.

Therefore, the triangle formed by the lines y = 0, 4x + 3y = 12, and 4x – 3y = –12 is a triangle with vertices at (0, 0), (3, 0), and (-3, 0).