Perpendicular lines are two lines that intersect at a right angle (90 degrees). When two lines are perpendicular, it means that they form four right angles where they intersect.

- Perpendicular lines have slopes that are negative reciprocals of each other. If the slope of one line is m, then the slope of the perpendicular line is -1/m.
- The product of the slopes of two perpendicular lines is -1.
- Perpendicular lines form right angles where they intersect.

Example 1: The lines y = 2x and y = -1/2x are perpendicular because the product of their slopes is -1.

Example 2: The lines x = 3 and y = 4 are perpendicular because one line is vertical (x = 3) and the other is horizontal (y = 4), and their intersection forms a right angle.

To determine if two lines are perpendicular, you can follow these steps:

- Find the slope of each line.
- Take the negative reciprocal of the slope for one of the lines.
- Compare the negative reciprocal with the slope of the other line. If they are equal, the lines are perpendicular.

1. Determine if the lines y = 3x + 2 and y = -1/3x - 4 are perpendicular.

2. Find the equation of a line that is perpendicular to y = 2x + 5 and passes through the point (3, 4).

3. Given the line 2x - 3y = 6, find the equation of a line perpendicular to it that passes through the point (4, -1).

4. Determine if the lines 3x - 4y = 8 and 4y = 3x - 5 are perpendicular.

Perpendicular lines intersect at right angles and have negative reciprocal slopes. To determine if two lines are perpendicular, compare the slopes using the negative reciprocal property.

Remember to practice solving problems involving perpendicular lines to strengthen your understanding of the concept.

.Study GuideAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 6 Curriculum Focal Points (NCTM)

Algebra: Writing, interpreting, and using mathematical expressions and equations

Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.