Hello friends, Previously we have discussed about probability examples and today we are going to learn about Graph and Math problems related to it., slope of lines for grade VIII of icse board. The slope of a line is generally represented by m. Simply slope is the rate at which the path of a line rises or decreases or the slope is a number that tells how steep the line goes up and down or slope is a ratio of vertical to horizontal distances. From the equation of a straight line (want to Learn more about Slope ,click here),
y = mx + b
Here the slope of line m is multiplied by x and b is the y-intercept where line crosses the y-axis. This is the equation of line and sensibly named as slope-intercept form. The graphical form of this equation can be quite straightforward, particularly if the values of m and b are relatively simple numbers. In the slope of line if the value of y changes then the value of x also changes. For example in the line y = (2/5) x – 3, here the slope is m = 2/5. This means that, starting at any point on this line, we can get to another point on the line by going up 2 units and then going to right 5 units. In other words, for every unit that x moves to the right, y goes up by two-fifths of unit. Now the formula of the slope of the line, if two points (x1,y1) and (x2,y2) are given then the slope m of the line is
m=y2-y1/x2-x1, (x1≠x2)
For example the slope of the line segment joining the points (1, - 6) and (- 6, 2). Here x1 =1, x2=-6, y1=-6 and y2=2, now using above formula
Slope= m=y2-y1/x2-x1
2+6/-6-1=- 8/7
So, m=- 8/7
The graphical form of slope is shown in the figure.
Now I am going to tell you the different types of slopes and their definitions. The different types of slopes are Slope of Parallel Lines, Slope of Perpendicular Lines and Negative Slope. Firstly the Parallel Lines, if the slopes of two lines are equal then these lines are parallel. The two parallel lines never intersect. If each line will cut the x axis at the same angle then slopes are
m1=tan x and m2=tan x
m1= m2
This shows that if two lines are parallel then their slope must be same.
The next is Slope of Perpendicular Lines. Perpendicular lines are lines which makes right angle at their intersection. Slope of Perpendicular is defined as if there is change in y co-ordinate then there is also change in x co-ordinate. On other hand, when two lines are perpendicular then the slope of one is the negative reciprocal of the other one. That is if the slope of one line is m then slope of the other is -1/m. -1/m is the slope of the other line is the negative reciprocal of m and is called negative slope. For example if the slope m=0.342 then the negative reciprocal of 0.342 is -1/0.342.
From the above discussion I hope that it would help you to understand the slope of lines and if anyone want to know about Permutations and combinations then they can refer to internet and text books for understanding it more precisely. Read more maths topics of different grades such as Factors and Number Sequences in Grade VIII in the next session here.
y = mx + b
Here the slope of line m is multiplied by x and b is the y-intercept where line crosses the y-axis. This is the equation of line and sensibly named as slope-intercept form. The graphical form of this equation can be quite straightforward, particularly if the values of m and b are relatively simple numbers. In the slope of line if the value of y changes then the value of x also changes. For example in the line y = (2/5) x – 3, here the slope is m = 2/5. This means that, starting at any point on this line, we can get to another point on the line by going up 2 units and then going to right 5 units. In other words, for every unit that x moves to the right, y goes up by two-fifths of unit. Now the formula of the slope of the line, if two points (x1,y1) and (x2,y2) are given then the slope m of the line is
m=y2-y1/x2-x1, (x1≠x2)
For example the slope of the line segment joining the points (1, - 6) and (- 6, 2). Here x1 =1, x2=-6, y1=-6 and y2=2, now using above formula
Slope= m=y2-y1/x2-x1
2+6/-6-1=- 8/7
So, m=- 8/7
The graphical form of slope is shown in the figure.
m1=tan x and m2=tan x
m1= m2
This shows that if two lines are parallel then their slope must be same.
The next is Slope of Perpendicular Lines. Perpendicular lines are lines which makes right angle at their intersection. Slope of Perpendicular is defined as if there is change in y co-ordinate then there is also change in x co-ordinate. On other hand, when two lines are perpendicular then the slope of one is the negative reciprocal of the other one. That is if the slope of one line is m then slope of the other is -1/m. -1/m is the slope of the other line is the negative reciprocal of m and is called negative slope. For example if the slope m=0.342 then the negative reciprocal of 0.342 is -1/0.342.
From the above discussion I hope that it would help you to understand the slope of lines and if anyone want to know about Permutations and combinations then they can refer to internet and text books for understanding it more precisely. Read more maths topics of different grades such as Factors and Number Sequences in Grade VIII in the next session here.
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