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x- and y-Intercepts Practice Problems

Fifteen hand-built problems on finding where a graph crosses the axes. They cover the set-the-other-variable-to-zero method on lines and parabolas, the fast intercept route through standard form, and the cases that catch people out — horizontal lines, vertical lines, and curves that never reach an axis.

  1. 1.

    Find the \(x\)-intercept of \(y = 2x - 6\). Give the \(x\)-value.

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    Set \(y = 0\): \(2x - 6 = 0\), so \(x = 3\). The point is \((3,\ 0)\).

  2. 2.

    Find the \(y\)-intercept of \(y = 2x - 6\). Give the \(y\)-value.

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    Set \(x = 0\): \(y = -6\). The point is \((0,\ -6)\) — for slope-intercept form it is just the constant.

  3. 3.

    Find the \(x\)-intercept of \(3x + 4y = 12\). Give the \(x\)-value.

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    Set \(y = 0\): \(3x = 12\), so \(x = 4\). In standard form the other term vanishes entirely.

  4. 4.

    Find the \(y\)-intercept of \(3x + 4y = 12\). Give the \(y\)-value.

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    Set \(x = 0\): \(4y = 12\), so \(y = 3\).

  5. 5.

    Find the \(y\)-intercept of \(y = -5x + 9\). Give the \(y\)-value.

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    The constant term: \(y = 9\), giving \((0,\ 9)\).

  6. 6.

    Find the \(x\)-intercept of \(y = -5x + 9\). Give the \(x\)-value.

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    \(-5x + 9 = 0\), so \(5x = 9\) and \(x = \dfrac{9}{5} = 1.8\).

  7. 7.

    Find the \(x\)-intercept of \(2x - 7y = 14\). Give the \(x\)-value.

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    Set \(y = 0\): \(2x = 14\), so \(x = 7\).

  8. 8.

    Find the \(y\)-intercept of \(2x - 7y = 14\). Give the \(y\)-value.

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    Set \(x = 0\): \(-7y = 14\), so \(y = -2\). Watch the sign on the negative coefficient.

  9. 9.

    Find the \(x\)-intercepts of \(y = x^2 - 9\). Give both \(x\)-values.

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    \(x^2 - 9 = 0\) factors as \((x - 3)(x + 3) = 0\), so \(x = 3\) and \(x = -3\). A parabola can cross the axis twice.

  10. 10.

    Find the \(x\)-intercepts of \(y = x^2 - 4x + 3\). Give both \(x\)-values.

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    \(x^2 - 4x + 3 = (x - 1)(x - 3) = 0\), so \(x = 1\) and \(x = 3\).

  11. 11.

    Find the \(y\)-intercept of \(y = x^2 - 4x + 3\). Give the \(y\)-value.

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    Set \(x = 0\): \(y = 3\). For any polynomial the \(y\)-intercept is the constant term.

  12. 12.

    How many \(x\)-intercepts does \(y = 5\) have?

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    None. The line is horizontal at height \(5\) and never reaches the \(x\)-axis. Its only intercept is the \(y\)-intercept \((0,\ 5)\).

  13. 13.

    How many \(y\)-intercepts does \(x = 4\) have?

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    None. The vertical line sits at \(x = 4\) and never reaches the \(y\)-axis. Its only intercept is \((4,\ 0)\).

  14. 14.

    How many real \(x\)-intercepts does \(y = x^2 + 4\) have?

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    \(x^2 + 4 = 0\) needs \(x^2 = -4\), which no real number satisfies. The parabola sits entirely above the axis, with its lowest point at \((0,\ 4)\).

  15. 15.

    A line has \(x\)-intercept \((6,\ 0)\) and \(y\)-intercept \((0,\ -4)\). Write it in slope-intercept form, giving only the right-hand side.

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    \(m = \dfrac{-4 - 0}{0 - 6} = \dfrac{-4}{-6} = \dfrac{2}{3}\), and the \(y\)-intercept is \(-4\), so \(y = \dfrac{2}{3}x - 4\).
M
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x- and y-Intercept Practice Problems

The x- and y-Intercepts lesson explains the method and what the points mean; this set is fifteen problems to practise on, each fully solved.

How to use this set

The whole topic runs on one idea: to find where a graph meets an axis, set the other variable to zero. Everything below is that idea applied to lines, standard form and parabolas.

Type just the value asked for. Where a problem wants two -values, separate them with a comma — 3, -3. Where it asks how many intercepts there are, type the count.

Common mistakes to watch for

Setting the wrong variable to zero. For the -intercept you set , not .

Sign slips on a negative coefficient. In , gives , so .

Assuming every graph has both. Horizontal and vertical lines each have only one.

Stopping at . No real solution means no real intercept — that is a complete answer.

Where to go next

Standard Form makes intercepts a one-step calculation, Slope-Intercept Form hands you the -intercept directly, and Slope is the other number you need to pin a line down.

Frequently Asked Questions

How do you find the x-intercept?+

Set and solve for . The -axis is the line where every point has , so that substitution finds exactly where the graph meets it.

How do you find the y-intercept?+

Set and solve for . In slope-intercept form it is simply , and for any polynomial it is the constant term.

Can a graph have no intercepts?+

Yes. A horizontal line with never crosses the -axis, a vertical line never crosses the -axis, and a parabola sitting entirely above the axis has no real -intercepts.

Can a graph have more than one x-intercept?+

Yes. A parabola usually has two, and higher-degree polynomials can have more. But a function can only ever have one -intercept, because is a single input and a function returns one output.

Why is standard form so quick for intercepts?+

In the two variables sit in separate terms, so setting one to zero deletes its term entirely and leaves a one-step division.

Should I answer with a point or a number?+

These problems ask for the single value, so type just the number — `3`, not `(3, 0)`. Where two values are wanted, separate them with a comma.

More practice problems

Slope Practice Problems Standard Form of a Line Practice Problems Slope-Intercept Form Practice Problems