Write the point-slope form of the equation of the line...

Write the point-slope form of the equation of the line satisfying each of the conditions. Then use the point-slope form to write the slope-intercept form of the equation in function notation.
Slope $=\frac{1}{5},$ passing through the origin

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Key Concepts

Point-Slope Form

A form of a linear equation that expresses the relationship using a given point and the slope of the line. This form is typically written as y - y? = m(x - x?), where m is the slope and (x?, y?) is any point on the line. It is especially useful when a specific point and the slope are known.

Slope-Intercept Form

A standard form of a linear equation that makes the slope and the y-intercept explicit. It is written as y = mx + b, where m represents the slope of the line and b is the y-intercept. This form provides a quick way to identify the gradient and the point at which the line crosses the y-axis.

Conversion Between Forms

The process of rearranging a linear equation from one form to another, such as converting from point-slope form to slope-intercept form. This involves algebraic manipulation to isolate y and express the relationship in a different yet equivalent way, which is useful for different applications or interpretations of the line's properties.

Function Notation

A method of writing functions that clearly denotes the dependent variable as a function of an independent variable, commonly written as f(x) rather than y. This notation is important in algebra and calculus as it emphasizes the functional relationship between variables.

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