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 $=3,$ passing through $(2,5)$

Key Concepts

Point-Slope Form

The point-slope form is an equation of a line that uses its slope and one point on the line to express the line's equation. Its general form is y - y? = m(x - x?), where m is the slope and (x?, y?) is a specific point on the line. This form is particularly useful when you know one point on the line and the slope, allowing you to quickly write an equation that describes the line.

Slope-Intercept Form

The slope-intercept form is a way to represent a linear equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept. This form provides a clear picture of how the line changes and where it crosses the y-axis, making it useful for graphing and understanding the behavior of the line.

Slope

The slope is a measure of the steepness and direction of a line. It is calculated as the ratio of the vertical change to the horizontal change between two points on the line. In any linear equation, the slope characterizes how much the output (y) changes for a given change in the input (x).

Function Notation

Function notation is a system for naming functions that explicitly shows the input and output relationship, often written as f(x). When expressing a linear equation in function notation, the equation takes the form f(x) = mx + b, which mirrors the slope-intercept form while signifying that the expression defines a function of x.

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