The city water department is proposing the construction of a...

The city water department is proposing the construction of a new water pipe. The new water pipe should be perpendicular to the old pipe. Use the graph below to write the equation for each water pipe.
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Key Concepts

Slope

Slope is a measure of the steepness and direction of a line in the coordinate plane. It is calculated as the ratio of the vertical change to the horizontal change between two distinct points on the line. Understanding slope is essential for determining how changes in one variable affect another and is key in analyzing linear relationships.

Linear Equations

Linear equations are algebraic equations that represent straight lines when graphed on the coordinate plane. They are typically expressed in forms such as slope-intercept form or point-slope form, which allow for easy identification of a line's slope and y-intercept. These equations model relationships with a constant rate of change.

Slope-Intercept Form

The slope-intercept form is a method of writing the equation of a line in the format y = mx + b, where m represents the slope and b represents the y-intercept. This form is useful for quickly identifying the key characteristics of a line, such as its steepness and where it crosses the y-axis.

Point-Slope Form

The point-slope form of a linear equation is used when the slope of the line and one point on the line are known. It is written as y - y? = m(x - x?), where m is the slope and (x?, y?) is the given point. This form is particularly useful for constructing the equation of a line from limited information.

Perpendicular Lines

Perpendicular lines are lines that intersect at a right angle (90 degrees). In coordinate geometry, two lines are perpendicular if the product of their slopes is -1, meaning their slopes are negative reciprocals of each other. This concept is important when determining the equation of a line that must form a right angle with a given line.

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