Lesson 6.3

Writing Equations from Slope & a Point

We know the direction (slope), but we don't know the start (y-intercept). We have to be detectives and find it.

Introduction

In the last lesson, we gave you specific instructions: "Start at 5." But real life isn't always that clear. Sometimes you know how fast you're going ($m$) and where you are right now $(x, y)$, but you don't know where you started ($b$).

Past Knowledge

Lesson 2.4 (Two-Step Equations). You need to be comfortable solving for a variable like $b$.

Today's Goal

Use to solve for , then write the full equation.

Future Success

This "Solve for b" strategy is used in chemistry to find initial concentrations.

Key Concepts

The "Find b" Strategy

We have 4 variables in our magic formula:

y

Have it

=
m

Have it

x

Have it

+
b

FIND ME

  1. Plug in your slope for .
  2. Plug in your point coordinates for and .
  3. Solve the equation for .
  4. Write the final equation with and .

Worked Examples

Example 1: Solving for b

Basic

Write equation: Slope , passes through .

Step 1: Plug in

Step 2: Solve

Subtract 2 from both sides.

Example 2: Negative Slope

Intermediate

Write equation: Slope , passes through .

Step 1: Plug in

Step 2: Solve

Add 6 to both sides.

Example 3: Fraction Slope

Advanced

Slope , point .

Step 1: Plug in

Half of 4 is 2.

Step 2: Solve

Subtract 2.

Common Pitfalls

Stopping Early

Students often find and circle it as the answer. The question asked for the Equation of the Line. You must write .

Switching X and Y

In the point , is x and is y. If you plug them into the wrong spots, will be wrong. Label your point first!

Real-Life Applications

Forensics: Identifying time of death.

  • The body cools at a specific rate (, slope).
  • The detective measures the current temperature () at a specific time ().
  • They solve for () to find the starting temperature (98.6°F) and check if the timeline matches.

Practice Quiz

Loading...