Question

Draw graph for equation given below:

3x + 2y = 6

Answer 1

The graph for the linear equation 3x + 2y = 6 is a straight line.

Step 1: Find the intercepts

To graph a line, it is usually easiest to find the points where it crosses the x and y axes.

X-intercept (set y = 0):

3x + 2(0) = 6

⇒ 3x = 6

⇒ x = 2

The x-intercept is at the point (2, 0).

Y-intercept (set x = 0):

3(0) + 2y = 6

⇒ 2y = 6

⇒ y = 3

The y-intercept is at the point (0, 3).

Step 2: Solve for y (Optional)

Writing the equation in slope-intercept form (y = mx + b) helps identify the slope:

2y = –3x + 6

⇒ y = –1.5x + 3

Slope (m): –1.5 or `-3/2`. This means for every 2 units you move right, you move 3 units down.

Y-intercept (b): 3.

Step 3: Plot and Draw

1. Mark the points (2, 0) and (0, 3) on a cartesian plane.

2. Draw a straight line passing through both points.