Question

Draw the graph of the following equation:

x = 3y

Answer 1

The graph of the equation x = 3y is a straight line passing through the origin (0, 0) with a slope of `1/3`.

Analysis of the equation

1. Isolate y: Divide both sides of the equation by 3.

`y = 1/3 x`

2. Identify Key Features:

1. Slope (m): The slope is `1/3`. This means for every 3 units moved to the right along the x-axis, the line rises 1 unit along the y-axis (“rise over run”).

2. yountercept (b): Since there is no constant term, the y-intercept is 0. The line passes through the point (0, 0).

Plotting Points

By substituting values for x, we can find corresponding coordinates to plot:

If x = 0, y = 0

⇒ (0, 0)

If x = 3, y = 1

⇒ (3, 1)

If x = 6, y = 2

⇒ (6, 2)

If x = –3, y = –1

⇒ (–3, –1)