General form (or) Standard form :
ax + by + c = 0
Slope intercept form :
y = mx + b
Point slope form :
(y - y_{1}) = m(x - x_{1})
Vertical line :
x = a
Horizontal line :
y = b
Example 1 :
A straight line with the gradient of -2 passes through the point (4, -1). Find the equation of the line in slope intercept form.
Solution :
Slope of the required line = -2
The required line is passing through the point (4, -1).
Equation of the line :
(y - y_{1}) = m(x - x_{1})
(y - (-1)) = -2(x - 4)
y + 1 = -2(x - 4)
Distributing -2, we get
y + 1 = -2x + 8
Subtract 1 on both sides, we get
y = -2x + 8 - 1
y = -2x + 7
Example 2 :
A straight line passes through the points A(1, 0) and B(3, 6). Find the gradient of the line and find equation in standard form.
Solution :
Slope (m) = (y_{2} - y_{1})/(x_{2} - x_{1})
Slope of the line joining the points A(1, 0) and B(3, 6).
x_{1} = 1, x_{2} = 3, y_{1} = 0 and y_{2} = 6
m = (6 - 0)/(3 - 1)
m = 6/2
m = 3
Equation of the line in slope intercept form :
y = mx + b
y = 3x + b ----(1)
Applying the point (1, 0), we get
0 = 3(1) + b
b = -3
Applying the value of b in (1), we get
y = 3x - 3 (Slope intercept form)
Converting into standard form, we get
3x - y - 3 = 0
Example 3 :
4x + 3y = 6 is a straight line. Find the gradient and y-intercept of the line.
Solution :
4x + 3y = 6
Subtracting 4x on both sides.
3y = -4x + 6
Dividing by 3 on both sides.
y = (-4/3)x + (6/3)
y = (-4/3)x + 2
Slope (m) = -4/3 and y-intercept = 2.
Example 4 :
Write the equation of the line which is parallel to the y-axis and passes through (1, 4)
Solution :
Equation of the line parallel to y-axis is y = 4.
Example 5 :
Write the equation of the line which is parallel to the x-axis and passes through (3, -5) ?
Solution :
Equation of the line parallel to x-axis is y = 3.
Example 6 :
Find the slope and y-intercept of the lines given below.
(i) 4x + y = 9
(ii) 3x - 2y = 4
Solution :
Converting the given standard form to slope intercept form, we can find slope and y-intercepts.
(i) 4x + y = 9
Subtract 4x on both sides.
y = -4x + 9
Comparing it into y = mx + b, we get
Slope = -4 and y-intercept = 9
(ii) 3x - 2y = 4
Add 2y on both sides.
3x = 2y + 4
Subtract 4 on both sides.
3x - 4 = 2y
Divide by 2 on both sides.
y = (3/2)x - (4/2)
y = (3/2)x - 2
Slope (m) = 3/2 and y-intercept = -2.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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