L6 · Characteristics of a Graph: Intercepts

Learning goal

“I can find the x- and y-intercepts of a linear relation from a graph description or an equation, state them as ordered pairs, and explain what each intercept means in a context.”

x-intercept — the x-coordinate where the graph crosses the x-axis; the point (a, 0). Found by setting y = 0.

y-intercept — the y-coordinate where the graph crosses the y-axis; the point (0, b). Found by setting x = 0. In y = mx + b it is the constant b.

Intercept as an ordered pair — intercepts are reported as points, e.g. (4, 0) and (0, -3), not as bare numbers, so the axis is never ambiguous.

Worked example

The line through (0, -2) and (4, 6). From the graph description: it crosses the y-axis at (0, -2), so the y-intercept is -2. Its slope is (6 - (-2)) / (4 - 0) = 2, so its equation is y = 2x - 2. For the x-intercept, set y = 0: 0 = 2x - 2 -> x = 1 - the point (1, 0). The method is always the same two moves: y-intercept - set x = 0 (or read the constant b); x-intercept - set y = 0 and solve.

Check yourself — explain it

To find the x-intercept you set y = 0 because...

Paired problem — example still visible

Find both intercepts of y = 3x - 6. -> y-intercept (0, -6); x-intercept: 0 = 3x - 6 -> x = 2 -> (2, 0)

Faded completion — last step is yours

"For y = -x + 5: y-intercept is (0, ___); x-intercept is (__, 0)." -> 5; 5

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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Grade 10 — Mathematics 10C › C10U07 Linear Relations & Functions

L6 · Characteristics of a Graph: Intercepts