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 in Exercises $1-28 .$ Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Slope $=-\frac{2}{3},$ passing through $(6,-2)$

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Key Concepts

Slope-Intercept Form

This is another common form for the equation of a line, where the equation is written as y = mx + b. Here, m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.

Linear Equation

A linear equation represents a straight line in the coordinate plane and expresses a constant relationship between the x and y variables. Understanding linear equations involves knowing how to manipulate and convert between various forms such as point-slope and slope-intercept.

Point-Slope Form

This is a format for writing the equation of a line when a point on the line and the slope are known. It is given by the expression y - y? = m(x - x?), where m represents the slope and (x?, y?) is any point on the line.

Slope

This measures how steep a line is, indicating the rate at which the y-value changes with respect to the x-value. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) and is essential for defining the direction and tilt of a line.

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