Mathematics
Grade 10
15 min
Slopes of parallel and perpendicular lines
Slopes of parallel and perpendicular lines
What you'll learn
- Identify and name at least 8 different polygons (triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon) with 100% accuracy when presented with a visual representation.
- Explain the relationship between the number of sides and the name of a polygon for at least 5 different polygons (triangle, quadrilateral, pentagon, hexagon, octagon) in their own words.
- Draw and label at least 3 different polygons (triangle, quadrilateral, pentagon) with the correct number of sides using a ruler with at least 80% accuracy.
- Compare and contrast a square and a rhombus, identifying the properties they share and the properties that make them different.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the slope of a line from its equation in any form.
Define the relationship between the slopes of parallel lines.
Define the relationship between the slopes of perpendicular lines.
Determine if two lines are parallel, perpendicular, or neither, given their equations.
Write the equation of a line that is parallel to a given line and passes through a specific point.
Write the equation of a line that is perpendicular to a given line and passes through a specific point.
Apply slope concepts to verify properties of geometric figures on the coordinate plane.
Have you ever noticed how the streets in a city grid are perfectly parallel or intersect at perfect right angles? 🏙️ That's geometry in action, and it's all about slope!
This tutorial w...
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Key Concepts & Vocabulary
TermDefinitionExample
SlopeA number that measures 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.A line passing through (2, 3) and (4, 7) has a slope m = (7-3)/(4-2) = 4/2 = 2.
Parallel LinesTwo or more lines in a plane that never intersect. They are always the same distance apart.The opposite sides of a rectangle are parallel.
Perpendicular LinesTwo lines that intersect to form a right angle (90 degrees).The x-axis and y-axis on the coordinate plane are perpendicular.
Slope-Intercept FormA common way to write the equation of a line: y = mx + b, where 'm' is the slope and 'b' is the y-intercept.In the equation y = -3x + 5, the slope is -3.
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Core Formulas
Slope Rule for Parallel Lines
If two non-vertical lines are parallel, then their slopes are equal. m_1 = m_2
Use this rule to check if two lines are parallel or to find the slope of a line that must be parallel to a given line. If the slopes are identical, the lines are parallel (assuming they have different y-intercepts).
Slope Rule for Perpendicular Lines
If two non-vertical lines are perpendicular, then the product of their slopes is -1. m_1 * m_2 = -1 or m_2 = -1/m_1
This means the slopes are negative reciprocals of each other. Use this rule to check if two lines are perpendicular or to find the slope of a line that must be perpendicular to a given line.
Special Case: Horizontal and Vertical Lines
A horizontal line (slope = 0) is perpendicular to a vertical lin...
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Challenging
For what value of 'k' is the line kx - 5y = 8 parallel to the line y = (3/5)x + 2?
A.5
B.3
C.-3
D.-5/3
Challenging
Find the value of 'k' such that the line 3x + ky = 5 is perpendicular to the line passing through the points (0, 2) and (3, 4).
A.2
B.-2
C.9/2
D.-9/2
Challenging
Line A has the equation y = (a/c)x + d. Line B is perpendicular to Line A and passes through the origin (0,0). What is the equation of Line B?
A.y = (-c/a)x
B.y = (c/a)x
C.y = (-a/c)x
D.y = (a/c)x
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What grade level is "Slopes of parallel and perpendicular lines"?
Slopes of parallel and perpendicular lines is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Slopes of parallel and perpendicular lines?
You'll be able to: Identify and name at least 8 different polygons (triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, nonagon, decagon) with 100% accuracy when presented with a visual representation; Explain the relationship between….
Is "Slopes of parallel and perpendicular lines" free to practice?
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How many practice questions are included with Slopes of parallel and perpendicular lines?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.