Question

Draw the graph of the following equation:

y = 2x

Answer 1

The graph of the equation y = 2x is a straight line passing through the origin.

Characteristics of the graph

1. Linear form: This is a linear equation in the slope-intercept form y = mx + b, where the slope m = 2 and the y-intercept b = 0.

2. The slope (m = 2): The slope represents the “steepness” of the line. For every 1 unit move to the right along the x-axis, the line rises 2 units along the y-axis. This positive slope indicates that the function is strictly increasing.

3. The intercepts: 

1. Y-Intercept: Since b = 0, the line crosses the y-axis at (0, 0).

2. X-Intercept: Setting y = 0 gives 0 = 2x, meaning the line also crosses the x-axis at the origin (0, 0).

4. Points on the line: By substituting values for x, we can find corresponding points to plot the line:

1. If x = 1

y = 2(1)

y = 2 

⇒ (1, 2)

2. If x = –1

y = 2(–1)

y = –2 

⇒ (–1, –2)

3. If x = 3

y = 2(3)

y = 6 

⇒ (3, 6)