|
Question 29088: How do you do 2x+y=5
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website!
2x+y=5
This is a linear equation in x and y
It is 2x+y-5 =0 which is of the form Ax+By+C =0
and is the general form of equation to a straight line.
2x+y=5
implies y = (-2)x+5
which is the slope and y-intercept form of the line.
When the coefficient of y is 1 on one side of the equation,the coefficient of x on the other side gives the slope and the free constant on the other side gives the y-intercept.
Therefore slope = -2 and y-intercept = 5
slope=(-2)<0 and slope negative implies the line traverses from the second quadrant to the fourth quadrant and the angle of inclination of the line with the x-axis is obtuse (more than 90 degrees)
y-intercept =(5)>0 implies that the portion =5 units cut off on the y-axis by the line is above the origin and therefore the line enters the fourth quadrant via the first quadrant.
Please draw the co-od axes and mark point B(0,5) on the y-axis.
Length OB = 5 where B is 5 units above the origin.
With these quick observations,you may give values to x and find the corresponding y's and then plot points (x,y) and join them all to give the graph of the line y =(-2)x+(5)
x=0,y=5 is what you have already got namely the point B=(0,5) on the y-axis
x=1, then y= 3. Therefore (1,3) is a point.
And so on.
Note: In case solving of x and y was the idea then you should be provided with one more linear equation in x and y so that the value for x and for y should hold good in both the equations.
Here is another similar problem which I have answered for some other student
x-2y=-3
This is a linear equation in x and y
It is x-2y+3 =0 which is of the form Ax+By+C =0
and is the general form of equation to a straight line.
x-2y=-3
implies x+3 = 2y
Dividing by 2
(1/2)x +(3/2) = y
That is y = (1/2)x +(3/2) which is the slope and y-intercept form of the line.
When the coefficient of y is 1 on one side of the equation,the coefficient of x on the other side gives the slope and the free constant on the other side gives the y-intercept.
Therefore slope = 1/2 and y-intercept =3/2
slope=(1/2)>0 and slope positive implies the line traverses from the first quadrant to the third quadrant
y-intercept =(3/2)>0 implies that the portion =3/2 units cut off on the y-axis by the line is above the origin and therefore the line enters the third quadrant via the second quadrant.
Please draw the co-od axes and mark point B(0,3/2) on the y-axis.
Length OB = 3/2 where B is 3/2 units above the origin.
slope = 1/2<1 and therefore the angle of inclination of the line with
the x-axis is less than 45 degree.
With these quick observations,you may give values to x and find the corresponding y's and then plot points (x,y) and join them all to give the graph of the line y =(1/2)x+(3/2)
x=0,y=3/2 is what you have already got namely the point B=(0,3/2) on the y-axis
x=1, then y= 2. Therefore (1,2) is a point.
And so on.
Note: In case solving of x and y was the idea then you should be provided with one more linear equation in x and y so that the value for x and for y should hold good in both the equations.
|
|
|
| |
