Dear grade 10 students we are providing detailed class notes for chapter 1 line segment topic – Slope of Parallel Lines based on Ontario curriculum. A key property of parallel lines is that they have the same slope. This chapter will cover how to determine the slope of parallel lines, apply it to equations of lines, and explore its real-world applications.
In coordinate geometry, the concept of parallel lines is fundamental in understanding the relationship between different lines on a Cartesian plane. A key property of parallel lines is that they have the same slope. These class notes will cover how to determine the slope of parallel lines, apply it to equations of lines, and explore its real-world applications.
Two lines are said to be parallel if they never intersect, no matter how far they are extended. In coordinate geometry, parallel lines have identical slopes but different y-intercepts.
For two lines with equations:
If the lines are parallel,
then: m1=m2
where:
The equations of the two lines below are parallel because they have the same slope:
Both lines have a slope of 3, so they will never intersect.
Given the equation of a line y = -2x + 4, find the slope of a parallel line.
Solution:
Find the equation of a line that is parallel to y=12x−3y = \frac{1}{2}x – 3 and passes through the point (4, 2).
Solution:
So, the equation of the parallel line is y=12xy = \frac{1}{2}x.
When two parallel lines are graphed on the Cartesian plane, they appear as distinct lines that never meet. Because they have the same slope, they rise and run at the same rate.
To graph parallel lines:
Parallel lines have the same m value but different b values. Slope of Parallel Lines
Example:
Both have m = 4, so they are parallel.
To check for parallel lines in standard form, convert the equation into slope-intercept form.
Example:
Rewriting both in slope-intercept form: y=−23x+2y = -\frac{2}{3}x + 2 y=−23x−32y = -\frac{2}{3}x – \frac{3}{2}
Since both have a slope of -2/3, they are parallel.
If given a line in point-slope form, the equation of a parallel line can be found using the same slope but a different point.
Example:
Highways and railway tracks are designed using parallel lines to ensure safe and efficient travel.
Buildings, bridges, and frameworks are designed with parallel beams and supports for stability and aesthetics.
Parallel lines are used in field markings for sports like basketball, soccer, and tennis. Slope of Parallel Lines
Designers and engineers use parallel lines to maintain symmetry and accuracy in technical drawings.
Understanding parallel lines and their slopes is an essential part of coordinate geometry. Parallel lines share the same slope, making them useful in various mathematical applications and real-life scenarios.
Chapter 1 Line Segment
1.1 Distance Between Two Points – class notes click here
1.2 Midpoint – class notes click here
1.3 Slope of a Line – class notes click here
1.4 Slopes of Parallel Lines – class notes click here
1.5 Slopes of Perpendicular Lines –class notes click here
1.1 Distance Between Two Points – quiz click here
1.2 Midpoint – quiz click here
1.3 Slope of a Line – quiz click here
1.4 Slopes of Parallel Lines – quiz click here
1.5 Slopes of Perpendicular Lines -quiz click here
Class 3 Hindi Chapter 2 Quiz Dear students and teachers of class 3 ,we are…
NCERT Class 3 Hindi Veena Chapter 2 Question Answers -We are providing question answers solutions…
Class 3 Hindi Chapter 1 Quiz We are excited to share helpful study resources for…
class 3 hindi chapter 1 solutions-सीखो (Veena). We are providing question answers for class 3…
DOE Mid Term Exam Syllabus & Date Sheet 2025–26 The Directorate of Education (DOE) has…
Class 4 Hindi Mid Term Mid-term examinations are a very important part of the academic…