Intercepts

Definition

Intercepts are points where a graph crosses the x-axis or y-axis. The x-intercept occurs when $y = 0$, and the y-intercept occurs when $x = 0$.

5 Must Know Facts For Your Next Test

1. To find the x-intercept, set $y=0$ in the equation of the line and solve for $x$.
2. To find the y-intercept, set $x=0$ in the equation of the line and solve for $y$.
3. A linear equation in slope-intercept form, $y = mx + b$, has a y-intercept at $(0, b)$.
4. A quadratic function can have up to two x-intercepts depending on its discriminant ($b^2 - 4ac$).
5. The intercepts provide key information about graphing equations and understanding their behavior.

Review Questions

• What is the x-intercept of the line given by the equation $3x + 4y = 12$?
• How do you find the y-intercept of a quadratic function?
• If a graph passes through $(0, -5)$, what does this point represent?

Related terms

Slope: The measure of steepness or incline of a line, represented as rise over run (change in $y$ over change in $x$).

Quadratic Equation: A polynomial equation of degree two that can be written in standard form as $ax^2 + bx + c = 0$.

Discriminant: In a quadratic equation, it is given by $b^2 - 4ac$ and determines the nature and number of roots.