Slope-intercept equation from slope and point | Algebra I | Khan Academy

TL;DR

The video explains how to find the equation of a line in slope-intercept form with a negative slope and a given point, using the formula y = mx + b.

Transcript

A line has a slope of negative 3/4 and goes through the point 0 comma 8. What is the equation of this line in slope-intercept form? So any line can be represented in slope-intercept form, is y is equal to mx plus b, where this m right over here, that is of the slope of the line. And this b over here, this is the y-intercept of the line. Let me draw... Read More

Key Insights

• 😃 Slope-intercept form represents a line's equation as y = mx + b, where m is the slope and b is the y-intercept.
• 🫥 A negative slope indicates a downward-sloping line, while a positive slope indicates an upward-sloping line.
• 🏙️ The y-intercept is the point where the line intersects the y-axis.

Questions & Answers

Q: What is the slope-intercept form of a line?

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. It allows us to easily determine the equation of a line.

Q: How does the slope affect the line?

The slope determines the steepness of the line. A negative slope indicates a downward-sloping line, while a positive slope indicates an upward-sloping line.

Q: What does the y-intercept represent?

The y-intercept represents the point where the line intersects the y-axis. It can be found by evaluating the equation when x=0, and the y-coordinate of the point will be the value of b in the slope-intercept form equation.

Q: How do you find the equation of a line with a negative slope and a given point?

Substitute the given slope and the y-coordinate of the given point into the slope-intercept form equation. The resulting equation will represent the line.

Summary & Key Takeaways

• A line's equation can be represented in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

• The slope is determined by the rise over run, and a negative slope means a downward-sloping line.

• The y-intercept is the point where the line intersects the y-axis.

• To find the equation of the line with a negative slope and a given point, substitute the slope value and the y-intercept value into the slope-intercept form equation.