To find equation of a line, we have different ways.
Point slope form :
If we have point on the line and slope, using the formula given below we find the equation of the line.
(y - y_{1}) = m(x - x_{1})
Slope intercept form :
If we have slope and y-intercept of the line, this formula can be used.
y = mx + b
Two point form :
If we see two points on the line, we use the formula given below.
(y - y_{1}) / (y_{2} - y_{1}) = (x - x_{1}) / (x_{2} - x_{1})
Problem 1 :
Solution :
Slope of a line = 1/3
y- Intercept (b) = 4
Equation of a straight line y = mx + b
M = 1/3t + 4
So, the required equation is M = 1/3t + 4
Problem 2 :
Solution:
x - intercept a = 3
N - intercept b = -2
By using x - intercept and y - intercept formula,
x/a + y/b = 1
x/3 + y(-2) = 1
x/3 - y/2 = 1
-y = -2/3x + 2
y = (2/3)x - 2
So, the required equation is y = (2/3)x - 2
Problem 3 :
Solution :
x - intercept form a = 4
y - intercept form b = 3
By using x - intercept and y - intercept formula,
x/a + y/b = 1
x/4 + y/3 = 1
y/3 = -x/4 + 1
y = (-3/4)x + 3
So, the required equation is y = (-3/4)x + 3
Problem 4 :
Solution :
In the figure given above, y-intercept is given and we have a point on the line.
(4, -2) and (0, 2)
m = (y_{2} - y_{1}) / (x_{2} - x_{1})
m = (2 + 2) / (0 - 4)
m = -4/4
m = -1
Equation of the line :
y - y_{1} = m(x - x_{1})
y - 4 = -1(x + 2)
y - 4 = -x - 2
y = -x - 2 + 4
y = -x + 2
Problem 5 :
Solution :
In figure, the straight line passes through two points (10, 8) and (0, 5)
(10, 8) and (0, 5)
m = (y_{2} - y_{1}) / (x_{2} - x_{1})
m = (5 - 8) / (0 - 10)
m = 3/10
Equation of the line :
y - y_{1} = m(x - x_{1})
y - 8 = (3/10)(x - 10)
10(y - 8) = 3(x - 10)
10y - 80 = -3x - 30
10y = -3x - 30 + 80
10y = -3x + 50
y = -(3/10)x + 5
Problem 6 :
Solution :
In figure, the straight line passes through two points (6, -4) and (0, -2)
(6, -4) and (0, -2)
m = (y_{2} - y_{1}) / (x_{2} - x_{1})
m = (2 + 4) / (0 - 6)
m = -6/6
m = -1
Equation of the line :
y - y_{1} = m(x - x_{1})
y + 4 = -1(x - 6)
y - 4 = -x + 6
y = -x + 6 + 4
y = -x + 10
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM