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 $=-\frac{2}{5},$ passing through $(15,-4)$

Key Concepts

Point-Slope Form

The point-slope form is a method for writing the equation of a line when you know one point on the line and its slope. It is generally represented as y - y? = m(x - x?), where (x?, y?) is the known point and m is the slope. This form is particularly useful when the information provided includes a specific point and the line's slope.

Slope-Intercept Form

The slope-intercept form expresses the equation of a line as y = mx + b, where m represents the slope and b represents the y-intercept, the point where the line crosses the y-axis. This form is widely used because it clearly shows both the slope and the starting value of y when x is zero, making it easy to graph and understand a line's behavior.

Slope

Slope is a fundamental concept in coordinate geometry that quantifies the steepness or angle of a line. It is calculated as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run) between any two points on the line. A negative slope indicates that the line falls as you move from left to right, while a positive slope indicates that it rises.

Function Notation

Function notation, typically written as f(x), provides a concise way to denote a function and its evaluation at any particular x-value. When dealing with linear equations, representing the equation in function notation, such as f(x) = mx + b, emphasizes that the equation defines a function mapping x-values to corresponding y-values, which is helpful in both analysis and graphing.

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