Method 1 :
The formula for slope is referred to rise over run,
Because the fraction consists of the rise (the change in y, going up or down) divided by the run (the change in x, going from left to the right).
The diagram shown below illustrates this.
The simplest way to look at the slope is
rise / run
(rise over run)
In the formula (rise / run), we can "rise" up or down... but, we ALWAYS "run" to the right.
Method 2 :
If a straight line is passing through the two points (x1, y1) and (x2, y2), then the formula to find the slope of the line is
m = (y2 - y1) / (x2 - x1)
Method 3 :
Let θ be the angle between the straight line "l" and the positive side of x - axis.
The figure given below illustrates this.
Then, the formula to find slope of the line is
m = tan θ
Method 4 :
If the equation of a straight line given in general form
ax + by + c = 0,
then, the formula to find slope of the line is
Method 5 :
If the equation of a straight line given in slope -intercept form
y = mx + b,
then, the slope of the line is 'm'.
To know the sign of the slope of a straight line, always we have to look at the straight line from left to right.
(i) If the line is going (from left to right) towards up, then the line is called rising line and its slope will be a positive value.
(ii) If the line is going (from left to right) towards down, then the line is called falling line and its slope will be a negative value.
(iii) If the line is horizontal, the slope will be zero.
(iv) If the line is vertical, the slope will be undefined.
Problem 1 :
What is the slope of a line whose inclination with positive direction of x -axis is
(i) 90° (ii) 0
Solution :
(i) θ = 90°
m = tan θ
m = tan 90°
m = undefined
(i) θ = 0°
m = tan θ
m = tan 0°
m = 0
Problem 2 :
What is the inclination of a line whose slope is (i) 0 (ii) 1
Solution :
(i) 0
m = 0
tan θ = 0
Hence the required angle of inclination is 0.
(ii) 1
m = 1
tan θ = 1
Hence the required angle of inclination is 45°.
Problem 3 :
Find the slope of a line joining the points
(i) (5, 5) with the origin
Solution :
m = (y2 - y1)/(x2 - x1)
x1 = 5, x2 = 0, y1 = 5 and y2 = 0
m = (0 - 5)/(0 - 5)
m = -5/(-5)
m = 1
(ii) (sin θ, -cos θ) and (-sin θ , cos θ)
Solution :
x1 = sin θ, x2 = -sin θ, y1 = -cos θ and y2 = cos θ
m = (cos θ - (-cos θ))/(-sin θ - sin θ)
m = (cos θ + cos θ)/(-sin θ - sin θ)
m = (2cos θ)/(-2sin θ)
m = -cos θ/sin θ
m = -cot θ
Problem 4 :
What is the slope of a line perpendicular to the line joining A(5, 1) and P where P is the mid-point of the segment joining (4,2) and (-6, 4) .
Solution :
P is the mid-point of the segment joining (4,2) and (-6, 4)
First, let us find the point P.
midpoint = (x1 + x2)/2, (y1 + y2)/2
= (4+(-6))/2, (2 + 4)/2
= -2/2, 6/2
= P(-1, 3)
Now, we have to find the slope of the line which is perpendicular to the line joining the points A(5, 1) and P(-1, 3).
Slope of AP x slope of the required line = -1
Slope of AP = (y2 - y1)/(x2 - x1)
Slope of AP = (3 - 1)/(-1 - 5)
= 2/(-6)
= -1/3
Slope of required line = -1/(-1/3)
= 3
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and Venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
©All rights reserved. onlinemath4all.com
May 23, 22 01:59 AM
Linear vs Exponential Growth - Concept - Examples
May 23, 22 01:42 AM
Exponential vs Linear Growth Worksheet
May 23, 22 01:34 AM
SAT Math Questions on Exponential vs Linear Growth