Question

Draw the graphs of the equations x = –3, y = 2 and 2x + 3y = 6. Write down the vertices of the triangle formed by these lines.

Answer 1

1. Plot the vertical line x = –3

The equation x = –3 represents a vertical line passing through –3 on the x-axis. For any value of y, x remains constant at –3.

2. Plot the horizontal line y = 2

The equation y = 2 represents a horizontal line passing through 2 on the y-axis. For any value of x, y remains constant at 2.

3. Plot the linear equation 2x + 3y = 6

To graph this line, find its intercepts:

x-intercept: Set y = 0

⇒ 2x + 3(0) = 6

⇒ 2x = 6

⇒ x = 3

Point: (3, 0)

y-intercept: Set x = 0

⇒ 2(0) + 3y = 6

⇒ 3y = 6

⇒ y = 2

Point: (0, 2)

4. Find the intersection points (Vertices)

The vertices of the triangle are the points where these three lines intersect:

1. Intersection of x = –3 and y = 2:

 Substituting the constant values directly gives the point (–3, 2).

2. Intersection of x = –3 and 2x + 3y = 6:

Substitute x = –3 into the equation:

2(–3) + 3y = 6

–6 + 3y = 6

3y = 12

⇒ y = 4

The vertex is (–3, 4).

3. Intersection of y = 2 and 2x + 3y = 6:

Substitute y = 2 into the equation:

2x + 3(2) = 6

2x + 6 = 6

2x = 0

⇒ x = 0

The vertex is (0, 2).

The coordinates of the vertices of the triangle formed by the lines are (–3, 2), (–3, 4) and (0, 2).