Lesson 5.10

Finding Intercepts

The fastest way to solve a line isn't to look at the whole thing. It's to make parts of it disappear.

Introduction

Every line crosses the axes somewhere. These crossing points are called Intercepts. At these special spots, one of the coordinates is always Zero.

Past Knowledge

Lesson 5.9 (Standard Form). Equations look like .

Today's Goal

Find X-intercepts by setting and Y-intercepts by setting .

Future Success

This "Zero Trick" works for EVERYTHING in math. Parabolas, circles, crazy curves... finding intercepts always starts with zero.

Key Concepts

The Cover-Up Method

To find one, hide the other.

Finding X-Intercept

You are on the X-axis, so height ($y$) is zero.

The term vanishes. Just solve for .

Finding Y-Intercept

You are on the Y-axis, so width ($x$) is zero.

The term vanishes. Just solve for .

Intercepts are Points: and .

Worked Examples

Example 1: Nice Numbers

Basic

Find intercepts for .

Find X-int

Cover up .

Divide by 2. . Point: .

Find Y-int

Cover up .

Divide by 3. . Point: .

Example 2: Watch the Negative

Intermediate

Find intercepts for .

Find X-int

Cover .

. Point: .

Find Y-int

Cover . Don't forget the negative sign!

Divide by -2. . Point: .

Example 3: Fractions Happen

Advanced

Find intercepts for .

Find X-int

(approx 2.33).

Find Y-int

(1.4).

Life isn't always integers. Fractions are valid intercepts.

Common Pitfalls

Mixing Them Up

Students confuse "x=0" with "x-intercept". Remember: To find X, kill Y. To find Y, kill X. It's opposite day.

Intercepts vs Coefficients

In , the x-intercept is 3 (because ). Some students just look at the equation and guess "2" because it's next to X. You must divide.

Real-Life Applications

Party Planning: You have $100 for pizza. Large pizzas cost $20 (), smalls cost $10 (). .

  • X-intercept (5, 0): You buy 5 Large and 0 Small.
  • Y-intercept (0, 10): You buy 0 Large and 10 Small.

Intercepts define the Extremes of your budget.

Practice Quiz

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