Writing equations in all forms | Algebra I | Khan Academy | Summary and Q&A

TL;DR

Learn how to find the equation of a line using three different forms: point slope form, slope intercept form, and standard form.

Key Insights

• 😥 Point slope form relates a specific point and the slope to the equation.
• 😃 Slope intercept form expresses the equation as y = mx + b, with m representing the slope and b as the y-intercept.
• ☺️ Standard form is represented as ax + by = c, and it does not have a direct interpretation on the graph.
• 💱 The slope can be calculated by finding the change in y and the change in x between two points on the line.
• 💁 To convert from point slope form to slope intercept form, distribute the slope and combine like terms.
• ❣️ Standard form requires rearranging the equation so that both x and y terms are on the same side.
• 🧑‍🏭 Multiplying all terms by a common factor can eliminate fractions in the equation.

Transcript

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Questions & Answers

Q: What is point slope form?

Point slope form relates a specific point on the line (x1, y1) and the slope (m) to the equation y - y1 = m(x - x1).

Q: How is slope intercept form different from point slope form?

Slope intercept form is written as y = mx + b, with m representing the slope and b representing the y-intercept. It does not require a specific point on the line.

Q: What does standard form mean for the equation of a line?

Standard form is expressed as ax + by = c, where a, b, and c are constants. This form does not have a direct interpretation on the graph.

Q: How can we find the slope of a line?

The slope (m) is determined by calculating the change in y divided by the change in x, represented as (y2 - y1) / (x2 - x1).

Summary & Key Takeaways

• There are three different forms of expressing the equation of a line: point slope form, slope intercept form, and standard form.

• Point slope form relates a point on the line and the slope of the line to the equation.

• Slope intercept form expresses the equation as y = mx + b, where m is the slope and b is the y-intercept.

• Standard form is ax + by = c, with a, b, and c being constants.