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. Then use the point-slope form of the equation to write the slope-intercept form of the equation.
Slope $=-\frac{3}{5},$ passing through $(10,-4)$

Key Concepts

Slope

The slope is a measure of the steepness or incline of a line, represented as the ratio of the vertical change to the horizontal change between any two points on the line. It is fundamental in understanding linear relationships, as it indicates the direction and rate at which the dependent variable changes with respect to the independent variable.

Conversion of Equation Forms

Converting the equation of a line from point-slope form to slope-intercept form involves algebraic manipulation to isolate y on one side of the equation. This process makes it easier to identify the y-intercept, as well as to graph the line, highlighting the relationship between different representations of linear equations.

Point-Slope Form

The point-slope form is an approach to writing the equation of a line when a point on the line and its slope are known. It is typically expressed as y - y? = m(x - x?), where m represents the slope and (x?, y?) is a specific point on the line. This form is particularly useful for quickly formulating a line's equation based on given conditions.

Slope-Intercept Form

The slope-intercept form of the equation of a line is written as y = mx + b, where m is the slope and b is the y-intercept, the point where the line crosses the y-axis. This form is valuable for graphing because it clearly shows both the slope and the point of intersection with the y-axis.

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