The equation of the straight line can be calculated in different ways according to the given condition. The different conditions of equation of straight line are given below:
When the angle is made in a straight line with x-axis making positive direction is said to be the inclination of a line. It is devoted by θ.
The tangent of the angle made by the straight line on the positive X-axis is called slope of the straight line. It is denoted by m. If θ be the angle made by the straight line AB on X-axis, then slope AB = m = tanθ
If three or more than three points lies in same straight line then it is said to be collinear points. We can prove the point P, Q, and R collinear by using slope as a slope of PQ = slope of QR =` slope of PR. As the points P, Q, and R in collinear. If the points P, Q, and R lie on the same line the slope of the two line will equal.
If the line AB cuts the X and Y - axis at the points A (a, O) and B(0, b) respectively. Then the length from the origin to the point of intersection of the line AB and X - axis is called the x -intercept and length from the point of intersection of the line AB and Y - axis are called y - intercept. In the figure , x -intercept OA = a and y -intercept OB = b.
Convention for the signs of intercepts
Let AB be a straight line parallel to X-axis. Then the ordinate of every point on the line XY is constant say b.
Let P(x, y) be any point on the lie AB. From P, draw PM perpendicular to X-axis, then MP = y.
∴ y = b, which is required equation of the line AB. The line AB. The line y = b lies above or below the X-axis according to as b is positive or negative.
If b = 0, then the line Ab coincides with X-axis. So, the equation of X-axis is y = 0.
Let AB be a straight line parallel to Y-axis. Then, the abscissa of every point on the line AB is constant, say a.
Let P(x, y) be any point on the AB. From P, draw PN perpendicular to Y-axis, then NP = x.
∴ x = a, which is required equation of the line AB. The line x = a lies to the right or left of Y-axis according to as a is positive or negative.
If a = 0, then the line Ab coincides with y-axis.
The equation of the straight line in the standard form: There are three standard forms of the equation of the straight line.They are:
Slope - intercept form: If the slope of the straight line m = tanθ and y - intercept (c) are known, the equation of the straight line in slope-intercept form is y = mx + c.
Here, given points (2,5)
The equation of the straight line parallel to y-axis is x=x coordinatesof given points
or, x=2
∴x-2=0Ans.
Here,
given points (5,-2)
The equation of the straight line parallel to y-axis is x=x coordinatesof given points
or, x=5
∴x-5=0Ans.
Given points,(-3,2)
The equation of the straight line parallel to x-axis is y=y-coordinates of the point.
or, y=2
∴ y-2=0.Ans.
Given points,(-3,2)
The equation of the straight line parallel to x-axis is y=y-coordinates of the point.
or, y=-4
∴ y+4=0.Ans.
Here,
The equation of the straight line parallel to x-axis and 4 units above the origin is y=4 and 4 units below the origin is y=-4.
∴The required equation are y-4=0 and y+4=0.Ans.
Here,
Angle on x-axis (θ)=45° and slope of the line(m)=tan 45θ°=1
Equation of straight line passing through origin is y=mx.
or, y=1,x
∴y-x=0.Ans.
Angle on x-axis (θ)=150°
∴ Slope (m)=tanθ=tan150°=-\(\frac{1}{√3}\)
Using formula,y=mx
y=-\(\frac{1}{√3}\)x
or,√3y=-x
∴x+√3y=0.Ans.
Here,
Given equation,x-y=5
or, -y=-x+5...........(i)
Comparing equation (i) with y = mx+c, we get
m=1 and c=-5
∴Slope (m)=1 and y-intercept (c)=-5.Ans.
Here given equation, y=√3 x or y=√3 x+0........(i)
Comparing equation (i) with y=mx +c,we get,
Slope (m)=√3 and y-intercept(c)=0 Ans.
The line AB whose point are A(0,1) and B(1,3) is produced to D(10,k).Find the value of k.
12
21
8
3
Find the value of x if the slope of the line joining the point A(1,3) and B(x,6) is 1.
9
10
2
4
The slope of the line joining A(-2,4) and B(3,5) is equal to the slope of the line joining C(0,4) and D(-3,k). Find the value of k.
17/6
17/5
11/5
12/5
Given points P(3,2) Q(0,-4) and R(-3,x) are collinear.Find the value of x.
x=-18
x=10
x=-10
x=-19
Given points (-5,1),(5,5) and (k,7) are collinear.Find the value of k.
k=10
k=-9
k=2
k=1
Find the equation of straight line having slope -3 and passing through (2,-2).
3x-y=2
3x+y=4
5x+y=4
3x-y=9
The straight line y =mx+6 passes through the points (1,4) and (-2,-5).Determine the equation of the straight line.
y=3x+1
y=3x-1
y=3x+7
y=2x+1
The straight line y =mx+6 passes through the points (3,4) and (-2,6).Determine the equation of the straight line.
2x+4y=26
2x-9y=21
2x-5y=12
2x+5y=26
Find the equation of a straight line making an angle 30° with X-axis and passing through the mid-point of the line joining (-2,3) and (8,5).
x√3-y=3+4√3
x√2-y=3-4√2
x√3-y=2-2√3
x√3-y=3-4√3
Find the equation of a straight line making an angle of 45° with X-axis and passing through the mid-point of the line joining (-2,3) and (4,1).
You must login to reply
Aiyaan
Find the equation of the line joining the origin and the points of trisection of join of (1,4) and (2,3).
Mar 31, 2017
0 Replies
Successfully Posted ...
Please Wait...
Popular Chaube
How to find out the equation of a straight line having equation and a point on X axis?
Mar 17, 2017
0 Replies
Successfully Posted ...
Please Wait...