Lesson 5.11

Graphing Standard Form

Don't rearrange the furniture if you don't have to. Graph directly using the Intercept Method.

Introduction

You have two choices with Standard Form: 1. Perform algebra to change it to Slope-Intercept Form (). 2. Find the two intercepts and connect these dots. Option 2 is usually faster.

Past Knowledge

Lesson 5.10 (Finding Intercepts). You need to be able to find and .

Today's Goal

Graph lines by plotting the x-intercept and y-intercept.

Future Success

This is the preferred method for graphing inequalities like .

Key Concepts

The Intercept Method

1

Find X-Intercept

Cover . Solve for . Plot on the horizontal axis.

2

Find Y-Intercept

Cover . Solve for . Plot on the vertical axis.

3

Connect

Draw a line through the two points.

Warning

If the line passes through , both intercepts are the same point! You need a second point by plugging in any number for .

Worked Examples

Example 1: The Nice Case

Basic

Graph .

X-int ()

. Plot .

Y-int ()

. Plot .

Connect

Draw the line.

Example 2: The Fraction Case

Intermediate

Graph .

X-int ()

. Plot .

Y-int ()

. Plot .

Wait, these weren't actually fractions. Because $10$ is divisible by both 2 and 5. Lucky us!

Example 3: A Point of View

Advanced

Graph .

Intercepts

.

.

Both intercepts are . We only have one dot!

Find a 2nd Point

Pick any . Let's try .

.

Plot point and connect to Origin.

Common Pitfalls

The "Slope" Confusion

In , the slope is NOT . In fact, the slope is . Don't try to identify slope directly unless you rearrange to . Just trust the intercepts.

Plotting on Wrong Axes

X-intercept goes on the horizontal axis. Y-intercept goes on the vertical axis. Students sometimes swap them.

Real-Life Applications

Maximizing Area: If you have 100 feet of fence for a rectangular garden (), the intercepts tell you the maximum possible Length (if Width is 0) and max Width (if Length is 0). Every point on the line is a valid shape you can build.

Practice Quiz

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