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

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June 12, 2010
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Writing equations in all forms | Algebra I | Khan Academy

## 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

• π₯ Point slope form relates a specific point and the slope to the equation.
• π Slope intercept form expresses the equation as y = mx + b, with m representing the slope and b as the y-intercept.
• βΊοΈ Standard form is represented as ax + by = c, and it does not have a direct interpretation on the graph.
• π± The slope can be calculated by finding the change in y and the change in x between two points on the line.
• π To convert from point slope form to slope intercept form, distribute the slope and combine like terms.
• β£οΈ Standard form requires rearranging the equation so that both x and y terms are on the same side.
• π§βπ­ Multiplying all terms by a common factor can eliminate fractions in the equation.

## Transcript

A line passes through the points negative 3, 6 and 6, 0. Find the equation of this line in point slope form, slope intercept form, standard form. And the way to think about these, these are just three different ways of writing the same equation. So if you give me one of them, we can manipulate it to get any of the other ones. But just so you know w... Read More

### 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.