Now let us draw the graphs of the equations y = x + 3, y = 2x + 5 and y = 3x − 2. See the figure and observe where these lines cut the y-axis.

Step-by-step solution

Idea: Every point on the y-axis has x = 0. So put x = 0 in each equation.

1. On the y-axis, x = 0. y = 2(0) + 5 = 5 → A (0, 5); y = 0 + 3 = 3 → B (0, 3); y = 3(0) − 2 = −2 → C (0, −2).1 mark
2. Each line y = ax + b cuts the y-axis at (0, b). The number b is called the y-intercept: 3 for y = x + 3 (3 units above the origin) and −2 for y = 3x − 2 (2 units below the origin).1 mark

Check: The y-coordinates 5, 3 and −2 are exactly the constant terms of the equations ✓.

Answer to write in the exam

Common mistakes that cost marks

• Putting y = 0 instead of x = 0. That gives where the line cuts the x-axis, not the y-axis.
• Writing C as (0, 2) and losing the sign of the constant −2.
• Writing the point as (5, 0) instead of (0, 5).

How this can come in the exam

Try one yourself

Write the y-intercepts of y = −x + 6 and y = 5x.

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