  # Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis and shade the triangular region.

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Updated on: September 25th, 2023 The coordinates of the vertices of the triangle formed by these lines and the x-axis and shade of the triangular region are (2, 3), (-1, 0), and (4, 0).

Given that, the equations for graphs are x – y + 1 = 0 and 3x + 2y – 12 = 0

Step 1: Now we have to find the table from the first equation that is x – y + 1 = 0

For, x – y + 1 = 0

On rearranging we get y = x + 1

 x 0 1 2 y 1 2 3

Step 2: Now we have to find the table from the second equation that is 3x + 2y – 12 = 0

For, 3x + 2y – 12 = 0

On rearranging we get y = ½ (12 – 3x)

 x 4 2 0 y 0 3 6

Step 3: Drawing the equations’ graph by using the values from the corresponding table

The equations’ graphical depiction is: We can see in the graphic that these lines cross each other at point

(2, 3) and x-axis at (-1, 0) and (4, 0)

therefore, the vertices of the triangle are (2, 3), (-1, 0), and (4, 0).

Summary:

## Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis and shade the triangular region.

The graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0 are mentioned above. The coordinates of the vertices of the triangle formed by these lines and the x-axis and shade of the triangular region are (2, 3), (-1, 0), and (4, 0)

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