Lesson 5.8

Graphing Slope-Intercept Form

Two steps: Begin and Move. It's the fastest way to draw a line without a calculator.

Introduction

Now that we can find and , let's put them to work. Graphing simply means finding two points and connecting them. The equation gives us those points instantly.

Past Knowledge

Lesson 5.7 (Slope-Intercept Form). You must be able to identify correctly to start.

Today's Goal

Graph lines by plotting the y-intercept first, then using the slope to find a second point.

Future Success

Later, we will graph inequalities by shading one side of this line.

Key Concepts

The "Begin-Move" Method

1

Begin with b

Plot the y-intercept on the vertical axis.

2

Move with m

Starting from , use to find the next point.

3

Connect

Draw a line through both points with arrows on the ends.

Worked Examples

Example 1: Positive Slope

Basic

Graph .

Step 1: Begin ()

. Plot point on the y-axis.

Step 2: Move ()

. Make it a fraction: .

Rise 2 (Up), Run 1 (Right).

Step 3: Draw

Connect intercepts.

Example 2: Negative Slope

Intermediate

Graph .

Step 1: Begin ()

. Plot .

Step 2: Move ()

.

Go DOWN 1, RIGHT 3.

Only the numerator is negative!

Example 3: Missing Parts

Advanced

Graph .

Analysis

There is no . This means .

(Begin at -2).

(Move 0 up, just go right).

Horizontal Line

Common Pitfalls

Starting at Origin

Students often start every graph at . You MUST start at . If , start at 3.

Going Left

For negative slope (like ), some students go Down AND Left. This makes a positive line. Always go Right for the Run.

Real-Life Applications

Cell Phone Plans: . Start at $10 (Base fee). For every gigabyte of data you use, move up $0.50. You can visually see which plan is better for low usage vs high usage.

Practice Quiz

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