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Point-Slope Form

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Point-Slope Form

Study Guide

Key Definition

The point-slope form of a line is given by $y - y_1 = m(x - x_1)$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

Important Notes

The slope $m$ represents the steepness of the line.
Point-slope form can be used to find the equation of a line given one point and the slope.
$y - y_1 = m(x - x_1)$ can be rearranged into slope-intercept form $y = mx + b$.
Always simplify the equation to make calculations easier.
Double-check your work by plugging the point back into the equation.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$m$ is the slope of the line

$(x_1, y_1)$ are the coordinates of a point on the line

$y = mx + b$ is the slope-intercept form

Remember to use proper notation when solving problems

Why It Works

The point-slope form directly uses the slope of the line and a specific point to define the line's equation. This makes it easy to derive the line's equation when you have these two components.

Remember

To convert from point-slope form to slope-intercept form, solve for $y$.

Quick Reference

Point-Slope Form:$y - y_1 = m(x - x_1)$

Slope-Intercept Form:$y = mx + b$

Understanding Point-Slope Form

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

In simple terms, the point-slope form is used to write the equation of a line when you know its slope and a point on it: $y - y_1 = m(x - x_1)$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the equation of a line with a slope of $\frac{-1}{2}$ passing through the point $(-3, 2)$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you are designing a skateboard ramp. The slope of the ramp is $\frac{3}{4}$ and it touches the ground at point $(0, 0)$. What is the equation of the ramp?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given two points on a line, $(1, 4)$ and $(3, 10)$, can you find the equation of the line using point-slope form?

Challenge Quiz

Single Choice Quiz

Advanced

What is the point-slope form of a line passing through $(-2, -1)$ with a slope of $5$?

Recap

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Review key concepts and takeaways