y-intercept

High School

Definition

In graphing, it is a point where the graph intersects with the y-axis (the vertical axis on a Cartesian plane).To find the y-intercept in a linear equation for example, substitute in 0 for the x value in your linear equation and you can then solve for y.

Worked examples

\(y = 2x + 5\) has y-intercept \((0, 5)\)

When \(x = 0\), \(y = 2(0) + 5 = 5\), so the graph crosses the y-axis at \((0, 5)\).

\(3x + 4y = 12 \)→\( 4y = 12 \)→\( y = 3\)

Substitute \(x = 0\) and solve for \(y\); the y-intercept is \((0, 3)\).

\(y = x^2 - 4\) has y-intercept \((0, -4)\)

Even for non-linear equations, plug in \(x = 0\) to find where the graph meets the y-axis.

Common mistakes

\(y = 3x + 7\) has y-intercept \(7\) → y-intercept is \((0, 7)\) The y-intercept is a point (ordered pair), not just the y-value alone.
To find y-intercept, set \(y = 0\) → Set \(x = 0\) and solve for \(y\) Setting \(y = 0\) finds the x-intercept, not the y-intercept.
\(2x + 3y = 6\) has y-intercept \((2, 0)\) → y-intercept is \((0, 2)\) Substitute \(x = 0\): \(3y = 6\) so \(y = 2\); \((2, 0)\) is the x-intercept.

Where you'll use it next

You'll use y-intercepts to sketch lines and curves, write equations in slope-intercept form, analyze functions, and interpret models in algebra, calculus, and applied sciences like physics and economics.

Found in 2 StudyPug lessons

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