How do you find the gradient of a straight line?
What is the use of finding gradient?
How can you explain gradient so that the ratio of change in y over change in x is not mixed up?
What is the purpose of finding y-intercept?
How do find the y-intercept?
What is the meaning of intercept?
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63 comments:
what i understand about the gradient of a straight line is a change in one quantity relative to another quantity remains constant.
Structural Engineer use gradient in constructing buildings.
space alien what do u mean by a change in one quantity relative to another...i dont fully understand..can u please expand on ur thoughts so that i can understand fully.
Gradient is found when there is a change in the Y values over the change in the X values.
to find the gradient of line first you hav to hav two points on that line and find the differences of the y points and diviode it by the differences of the x points.
To space_alien:
Are u confused by the fact that the gradient is delta Y divided delta X????
ratman a change in one quantity relative to another means the first quantity is divides by the second quantity,e.g. distance/time.
the use of finding a gradient is to know for example if a plane is taking off or landing it has to the pilot has to know what gradint to land at or to take off at.
to brainiac what do you mean by delta y / delta x
To tell the truth i don't know how to find the y-intercept.
Elmo:
I think u are confusing urself with the angles of elevation/depression to gradient of a straight line....Correct me if i'm wrong plz..
space_alien
delta y / delta x simnply means the change of y divided by the change of x
to elmo y-intercept mean where a line or curve cuts the y-axis.This what i understand about by the y-intercept
Brainiac that's true elmo. The gradient or slope of something in graphical terms is the speed of change, That's what i believe
Space_alien: It means a change in Y points over the change in the X points...Do you understand now???
eg gradient = Y2 - Y1
_______
X2 - X1
To Eervyone:
Do a curve graph always have to cut the y-axis???
to brainaic
what can Y2 and Y1 be represented by in the real world.
The ratio of a change in Y over the change in X can be easily done simply by appointing a single number to each of the co-ordinates of the first point and by doing tyhe same for the second point except by using a different number
To Space_alien:
In real world Y2 and Y1 could be used in finding the location of a particular part of the world in the navigation field by the usage of the lines of longitude and latitude.
no the graf does not always cut the y axis....think bout it...like a parabola or sumthing...
to ans elmo:
ways to calulate the y intercept would be to work out the equation
y=mx+c...if the y intercept is c and you have y and x values and the gradient is m...plug in those values and then solve for c
and then you could use the graf method...i am not entirely sure how to explain that method so the first one to read this comment has that responsiblity....lol!
i don't understand the third question fully. Can someone explain it in simpler terms?
elmo the y intercept as they said before is where the line cuts on the yintercept. whever it be on the y intercept. as blessed08 said before. just plug in the equation and u'll see it.
y=mx+c
where c represents the y intercept.
think u understand it clearer
HELLION
How can you explain gradient so that the ratio of change in y over change in x is not mixed up?
MS WAS JUST ASKING THAT WITHOUT MIXING UP X FOR Y AND VICE VERSA. TO GET THE GRADIENT. BECAUSE SOME PEOPLE DO GET MIX UP
REMEMBER THE FORMULA IS Y2-Y1 ALL OVER X2-X1
Anyone who could answer
Ms Fariel also
i dont really know what is the purpose of finding the y intercept
the meaning of intercept is where two lines meet at any point
To marz
the purpose of finding the y intercept is to show the value of the function, when the independent variable is equal to zero
Yes blessed08 spacealien and marz y=mx+c is the equation of a line
lets take for example a straight line and the term y intercept
If a line is cutting the y-axis we are sure that x will be equal to zero therefore the constant (c)will be the the point on the y-axis
We all know the gradient formula
y2-y1/x2-x1
what we need to say is gradient of a straight line passing throught 2 points
Refering to past and present questions from various bloggers
yes there are positive and negative gradients
To find the gradient you first need 2 values of X an 2 values of Y an then you say Y2-Y1 divide X2-X1
The purpose of of the gradient is to find out how much a line is sloping
elmo u said that u dont know how to find the y intercept..u shud know that the equation of a line is y=mx+c, where m is the gradient and c is the y intercept. lines can also have the form Ax + By + C = 0. from this u can say that y = -Ax/B - C/B. m(gradient) = -A/B and c(y intercept) = -C/B
the y intercept is where the line cuts at the y axis and it also where x = 0.
To my knowledge, gradient is the change in the y axis divided by the change in x axis, or the horizontal rise over the vertical run,
but basically what this says is that the gradient of a straight is the biggest value on the y axis minus(-) the smallest value on the y axis, divided by the biggest value on the x axis minus(-) the smallest value on the x axis.
e.g. if the y value is 5 and 10 and the x value is 4 and 9 then the gradient is 5-10 divided by 9-4 which is 5 divided by 5 which is 1. so the gradient in this case is 1.
you should always remember that when u dividing to find gradient, the y which vertical is always on top the x which is horizontal
e.g. when u feeling tired and you going to lie down on your bed, you are standing upright which is vertical and then u lie down which is horizontal. same thing with y and x. the y is upright and then it lie down and is call x so y is on top of x in finding gradient of a straight line. NB. when naming the points u go in alphabetical order i.e x then y.
Brainiac
a curve doen't have to cut the y-axis,reason being is when there is no zero value for x.
according to mathworm.
u can use the formula y=mx+c to find the gradient of a straight line. m represents the gradient and c is the y-intercept which is where the line cuts the y axis and x=0.
m is calculated by y2-y1/x2-x1 . in this way the change in y over the change in x is not mixed up.
The Intercept is the point at which the X an Y axis meet
To find the Y intercept you look for the point at which X is zero
To find the gradient of change in the y-axis and divide it by the change in the x-axis.
The elements that are used to find the gradient are the change in the y and x-axis.
to answer miss' third question i guess....to explain it so that it cannot be mixed up...is to see it as y on the graph is ontop...{thats more of a pattern}
To explain gradient so that the ratio of change in y over the change in x is not mixed up is by stating that gradient represents the slope of a graph. Hence the y-axis which represents 'high ground' must be first taken into consideration
i agree with braniac that a curve dosent have to cut the y axis it can exist in a particular quadrant without cuttin any axis.
To everyone
I am seeing that u all are responding on whether a curve or line can cut the x or y axis.
My question is that does a line or curve need to cut any of the axis?
Can it lie within the x and y axis?
brainiac and space alien
U are both confusing me. When u all speak of Y1 and Y2.
I am so confused that I can't even ask a question.
Please explain.
top shottar
yes two lines can be with the x and y axis. however you would have alot of x and y values
eg.
x,y
0,1
2,4
4,6
etc
The gradient of a straight line is found by a change in the y axis over a change in the x axis.
To notice
I must say that it does no matter on whether u minus the bigger value from the smaller valueor vice versa the result is the same constant.
gradient is found by the rise of the y axis over the run of the x axis
the use to finding the gradient is to sub in the equation to get y =mx +c
the gradiant of a straigt line is simly the rate of change of the variable on the y axis divided by the rate of change of the variable on the x axis
gradiant= change in y variable / chane in x variable
the y-intercept can found by taking the point at which the line on graph cuts the y-axis
To xm2
Can u explain further on what is the rise and run of the x and y axis so that I would be able to understand clearly.
I am a bit confused to the deffinition that u gave.
To xm2
The deffinition that u gave about the use of finding gradient is a bit too Mathematically inclined.
Then I would like to ask does the equation y=mx+c exist in real life?
How could this be of importance in real life?
in drawing a srtaight line to connect the points on a graph when this line crosses the y axis or the x axis this point is called the intercept point
Gradient is slope. Constant gradient is slope in a straightline which is uniform. Gradient in is the dfference in "y" over "x". {y2-y1}/{x2-X1}
To everyone
What about the gradient of a curve?
Why is it necessary to find this in Maths? I am always wondering if this is important or even used in the industry since it is so difficult to understand or even solve a question of this kind in Maths.
WHEN DO WE USE IT IN REAL LIFE?
Top shottar..the term gradiant is very important in everyday life. think about it. If there was no gradiant then there wouldnt be a change in anything. for example...the land would be flat..there would be no hills or no inclines. or if u were travelling in a car there wouldnt be an increase or decrease in the speed of the car.
intercept is a point or place where something e.g a line may cross a border e.g the y-axis
the word intercept means the point at which the graph cuts the y axis. Suggestions anyone????
you find gradient by equating the cchange in vertical heigth divided by the change in horizontal extension or length
the gradient of a straight line is found by firstly choosing two points on the line. the x and y coordinates of these points are then determined. the gradient is the difference in the y coordinates divided by the difference in the x coordinates.
y intercept can be found in several ways.
1)from the graph read off the value where the grapg cuts the y axis.
2)by using the equation y=mx+c substitute values of gradiant(m), a x value and a y value. c represents the y intercept
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