How to find the slope with angle of inclination :
Actually we follow four methods to find the slope of the line
(i) Slope using angle of inclination (m = tan θ)
(ii) Slope with two points lies on the line
m = (y2 - y1)/(x2-x1)
(iii) Slope by comparing the equation with y = mx + b
(iv) Slope using the formula
m = -coefficient of y/coefficient of x
Here we are going to see how to find the slope with angle of inclination.
Example 1 :
Find the slope of the straight line whose angle of inclination is 30°
Solution :
Angle of inclination (θ) = 30°
Slope (m) = tan θ
Instead of applying θ as 30°, we get
m = tan 30°
m = 1/√3
Example 2 :
Find the slope of the straight line whose angle of inclination is 60°
Solution :
Angle of inclination (θ) = 60°
Slope (m) = tan θ
Instead of applying θ as 60°, we get
m = tan 60°
m = √3
Example 3 :
Find the slope of the straight line whose angle of inclination is 90°
Solution :
Angle of inclination (θ) = 90°
Slope (m) = tan θ
Instead of applying θ as 90°, we get
m = tan 90°
m = ∞
Example 4 :
Find the slope of the straight line whose angle of inclination is 45°
Solution :
Angle of inclination (θ) = 45°
Slope (m) = tan θ
Instead of applying θ as 45°, we get
m = tan 45°
m = 1
Example 5 :
The side AB of a square ABCD is parallel to x-axis . Find the
(i) slope of AB
(ii) slope of BC
(iii) slope of the diagonal AC
Solution :
(i) Slope of AB
Since the side AB is parallel to x-axis, angle formed by the side AB with x-axis is zero.
So, slope of the side AB (m) = tan 0° = 0
Hence slope of AB is 0.
(ii) Slope of BC :
If the side AB is parallel to x-axis, then the side BC will be perpendicular to x-axis.
So it forms the angle 90° with axis.
m = tan 90° = ∞
Hence the slope of the side BC is ∞
(ii) Slope of the diagonal AC :
Since the side AC is diagonal, the angle of inclination of the side AC with x-axis is 45°
m = tan 45° = 1
Hence the slope of the side AC is 1.
After having gone through the stuff given on "How to find the slope with angle of inclination", we hope that the students would have understood how to solve problems using unit rates.
Apart from the stuff given above, if you want to know more about "How to find the slope with angle of inclination", please click here
Apart from the stuff given on "How to find the slope with angle of inclination", if you need any other stuff in math, please use our google custom search here.
WORD PROBLEMS
HCF and LCM 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 fractrions
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