The y-intercept is the value of y when x is zero. In a real situation it is the starting amount, and your task is to say so in words with the correct unit.
How do you turn the number into a meaning?
Use a sentence frame: “When [x quantity] is 0, [y quantity] is [value and unit], so this is the [starting amount].”
This forces you to name both quantities and to think about what zero means for x.
Worked example
An original taxi fare graph is a straight line through (0, 3) and (4, 9). The fare is in ringgit and the distance in kilometres.
The intercept is 3, because the line crosses the y-axis at (0, 3). In context: when the distance is 0 km, the fare is RM3, so RM3 is the starting fare.
The gradient is (9 − 3) ÷ (4 − 0) = 6 ÷ 4 = 1.5. In context: the fare rises by RM1.50 for each extra kilometre.
The two pieces give the equation C = 1.5d + 3. Check at d = 4: 1.5 × 4 + 3 = 9. This matches the point (4, 9).
A second situation uses a phone plan graph through (0, 20) and (10, 25). The intercept 20 means a monthly base plan of RM20 when 0 GB of extra data is used. The gradient (25 − 20) ÷ 10 = 0.5 means RM0.50 per extra GB.
What does the common mistake look like?
A student reads the taxi graph and says the intercept is RM1.50 per kilometre. That is the gradient. The student has confused the rate with the starting value.
A quick test: the intercept belongs to x = 0 and has the unit of y, which is ringgit. The gradient has a compound unit, ringgit per kilometre. Checking units separates them.
Steps to follow
- Find the point where the line crosses the y-axis and read its y value.
- Write the meaning using the frame: when x is 0, y is the value.
- Check the unit: the intercept has the same unit as the y-axis quantity.
Self-check
A graph shows the height of a candle (cm) against the time it burns (hours). The line passes through (0, 20) and (4, 12). State the intercept and the gradient with their meanings.
Answer
Intercept: when the time is 0 hours, the height is 20 cm, so the candle starts 20 cm tall. Gradient: (12 − 20) ÷ (4 − 0) = −8 ÷ 4 = −2.
The negative sign means the height falls by 2 cm each hour. Check: after 4 hours, 20 − 2 × 4 = 12 cm, which matches the graph.
Where to go next
Together, gradient and intercept describe the whole line, which leads into linear law in Additional Mathematics. The linear law axes explorer lets you try this on changing lines. If the gradient step is uncertain, revisit calculating a straight-line gradient. Mathematics tuition can apply the same skill to your own graph questions.