Slope-intercept equation from a graph examples | Algebra I | Khan Academy

TL;DR

This video explains how to find the slope and y-intercept of a linear equation and how to graph various lines.

Transcript

So you may or may not already know that any linear equation can be written in the form y is equal to mx plus b. Where m is the slope of the line. The same slope that we've been dealing with the last few videos. The rise over run of the line. Or the inclination of the line. And b is the y-intercept. I think it's pretty easy to verify that b is a y-i... Read More

Key Insights

• 😃 The equation y = mx + b represents linear equations and can be used to find the slope and y-intercept.
• ❣️ The y-intercept is the point where the line intersects the y-axis, which can be determined by substituting x = 0 into the equation.
• 💱 The slope is the change in y for every unit change in x and can be calculated using two points on the line.

Questions & Answers

Q: How do you determine the y-intercept of a linear equation?

To find the y-intercept, substitute x = 0 in the equation. The resulting value of y will be the point where the line intersects the y-axis.

Q: What does the slope represent in a linear equation?

The slope represents the change in y for every unit change in x. It indicates the inclination or steepness of the line.

Q: How do you calculate the slope using two points on a line?

Choose two points (x₁, y₁) and (x₂, y₂) on the line. The slope is determined by the formula: (y₂ - y₁) / (x₂ - x₁).

Q: Can the slope of a line be negative?

Yes, the slope can be positive, negative, or zero. A positive slope indicates an upward direction, a negative slope indicates a downward direction, and a slope of zero indicates a horizontal line.

Summary & Key Takeaways

• Linear equations can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

• The slope is the inclination or rise over run of the line, while the y-intercept is the point at which the line intersects the y-axis.

• By using specific points on a line, we can calculate the slope and y-intercept of the equation.