Understand intercept
Objective. Identify and interpret the y-intercept.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
The y-intercept is the point where a straight line crosses the y-axis, occurring exactly where x = 0. In the equation y = mx + c, the value c directly gives the y-intercept, so reading or substituting x = 0 reveals it instantly. For y = 4x − 7, substituting x = 0 gives y = −7, so the line crosses the y-axis at (0, −7). Always check the constant term's sign carefully, since it can be easy to misread.
Worked example
State the y-intercept of the line with equation y = 5x + 3.
- 1Substitute x = 0 into the equation: y = 5(0) + 3
- 2Simplify: y = 0 + 3
- 3So y = 3 when x = 0
- 4The y-intercept is (0, 3)
Answer: (0, 3)
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes read the x-intercept from a graph and call it the y-intercept, confusing the two axes. Always confirm the y-intercept is where the line crosses the vertical axis, at x = 0.
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