Problems 95-104 are based on material learned earlier in the...

Problems $95-104$ are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. $$ \text { Find an equation of the line that contains the point }(2,-3) \text { and is perpendicular to the line } 5 x-2 y=6 $$

Problems $95-104$ are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
$$
\text { Find an equation of the line that contains the point }(2,-3) \text { and is perpendicular to the line } 5 x-2 y=6
$$

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Key Concepts

Slope

Slope is a measure of the steepness and direction of a line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Understanding the slope allows us to analyze the line's behavior, such as its angle relative to the horizontal axis, and is fundamental in determining relationships between lines, such as parallelism and perpendicularity.

Perpendicular Lines

Perpendicular lines are lines that intersect at a right angle (90 degrees). A key property of perpendicular lines is that their slopes are negative reciprocals of each other. This means if one line has a slope of m, the line perpendicular to it will have a slope of -1/m, provided m is not zero. This concept is critical when determining the equation of a line that must be perpendicular to a given line.

Point-Slope Form

The point-slope form of a line is a useful equation format when you know a point on the line and its slope. It is typically written as y - y? = m(x - x?), where (x?, y?) is a known point on the line and m is the slope. This form is particularly powerful in constructing the equation of a line when specific information about a point and the line's orientation is given.

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