Sample Problems on Slope of a Line
Problem 1: Find the slope of points (1,2) and (2,3).
Solution:
As slope is given as m = (y2 – y1)/(x2 – x1)
⇒ m = (3 – 2)/(2 – 1)
⇒ m = 1
Problem 2: Find the value of x if the slope is 2 and points are (2,2) and (x,6).
Solution:
m = (y2 – y1)/(x2 – x1)
⇒ 2 = (6 – 2)/(x – 2)
⇒ 4 = 2(x-2)
⇒ x-2 = 2
⇒ x = 4
Problem 3: Find the value of y if slope is 3 and points are (2,13) and (4, y).
Solution:
m = (y2 – y1)/(x2 – x1)
⇒ 3 = (y – 13)/(4 – 2)
⇒ y – 13 = 3(2)
⇒ y – 13 = 6
⇒ y = 6 + 13 = 19
Problem 4: Find the line passing from coordinates (2,5) and the slope of a line is 5.
Solution:
Slope m = 4
y – y1= m (x – x1)
We know slope m = 5 and point (x1, y1) = (2,5)
Now putting these value in equation
⇒ y – 5 = 5 x (x – 2)
⇒ y – 5 = 5x – 10
⇒ y = 5x – 10 + 5
⇒ y = 5x -5
Slope of a Line
Slope of a Line is the measure of the steepness of a line a surface or a curve whichever is the point of consideration. The slope of a Line is a fundamental concept in the stream of calculus or coordinate geometry or we can say the slope of a line is fundamental to the complete mathematics subject. The understanding of slope helps us solve many problems in mathematics, physics, or engineering.
In this article, we will learn about the slope of a line in detail, slope of a straight line with its various methods of calculations, and also the equation for the slope of a line.
Table of Content
- What is a Slope?
- What is the Slope of a Line?
- Slope of a Line Equation
- How to Find Slope of a Line?
- Calculation of Slope between Two Points
- Calculation of Slopes from Graph
- Calculation of Slope from Table
- Positive and Negative Slope
- Slopes of Different Lines
- Slope of Horizontal Line
- Slope of Vertical Line
- Slope of Perpendicular Lines
- Slope of Parallel Lines
- Equation of Line in Slope Intercept Form