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
8
21
3
Find the value of x if the slope of the line joining the point A(1,3) and B(x,6) is 1.
10
9
4
2
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.
11/5
17/6
17/5
12/5
Given points P(3,2) Q(0,-4) and R(-3,x) are collinear.Find the value of x.
x=-19
x=10
x=-10
x=-18
Given points (-5,1),(5,5) and (k,7) are collinear.Find the value of k.
k=1
k=2
k=10
k=-9
Find the equation of straight line having slope -3 and passing through (2,-2).
3x-y=9
5x+y=4
3x+y=4
3x-y=2
The straight line y =mx+6 passes through the points (1,4) and (-2,-5).Determine the equation of the straight line.
y=3x+7
y=2x+1
y=3x-1
y=3x+1
The straight line y =mx+6 passes through the points (3,4) and (-2,6).Determine the equation of the straight line.
2x-9y=21
2x-5y=12
2x+4y=26
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=2-2√3
x√2-y=3-4√2
x√3-y=3-4√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).
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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
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Popular Chaube
How to find out the equation of a straight line having equation and a point on X axis?
Mar 17, 2017
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