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y-Intercepts

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y-Intercepts

Study Guide

Key Definition

The y-intercept of a graph is the point where the graph crosses the y-axis. In the equation $y = mx + b$, the y-intercept is $b$.

Important Notes

A linear function has at most one y-intercept.
In the equation $y = mx + b$, $b$ is the y-intercept.
Quadratic equations in the form $y = ax^2 + bx + c$ have y-intercept $c$.
The y-intercept is where $x = 0$.
On a graph, the y-intercept is the point $(0, b)$.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

$y = mx + b$ is the slope-intercept form of a linear equation

Remember to use proper notation when solving problems

Why It Works

The y-intercept is determined by setting $x = 0$ in the equation, isolating the constant term as the y-value.

Remember

For linear equations, quickly find the y-intercept from the equation: it's the $b$ in $y = mx + b$.

Quick Reference

Linear Equation:$y = mx + b$

Quadratic Equation:$y = ax^2 + bx + c$

Understanding y-Intercepts

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The y-intercept is the point on the y-axis where a line crosses, represented by $b$ in $y = mx + b$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the y-intercept of the line $y = 2x + 3$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A skateboard ramp is designed with the equation $y = -0.5x + 4$. What is the y-intercept and what does it represent?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given the quadratic equation $y = x^2 - 4x + 7$, find the y-intercept.

Challenge Quiz

Single Choice Quiz

Advanced

For the function $y = 3x^2 - 2x + 5$, what is the y-intercept?

Recap

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Review key concepts and takeaways