REVIEW
Slope of a Line: If a line passes through two distinct points P_{1}(x_{1} , y_{1}) and P_{2}(x_{2}, y_{2}), its slope is given by:
m = (y_{2}  y_{1}) / (x_{2}  x_{1})
with x_{2} not equal to x_{1}.
This is another interactive tutorial on the slope of a line.
General Equation of a Straight line:
The general equation of straight line is given by:
Ax + By = C
where A, B and C are constants and A and B cannot be both zero.
For an interactive exploration of this equation Go here.
Any straight line in a rectangular system has an equation
of the form given above.
Slope intercept form of a Line:
The equation of a line with a defined slope m can also be written as follows:
y = mx + b
where m is the slope of the line and b is the y intercept of the graph of the line.
The above form is called the slope intercept form of a line. To understand why, go to this interactive tutorial.
PointSlope form of a line:
An equation of a line through a point P(x_{1} , y_{1})
with slope m is given by
y  y_{1} = m(x  x_{1})
Vertical and Horizontal lines:
a  If we set A to zero in the general equation, we obtain an equation in y only of the form
By = C
which gives y = C/B = k; k is a constant. This is a horizontal line with slope 0 and passes through all points with y coordinate equal to k.
b  If we set B to zero in the general equation, we obtain
Ax = C
which gives x = C/A = h; h is constant. This is a vertical line with undefined slope and passes through all points with x coordinate equal to h.
Parallel Lines:
Two non vertical lines are parallel if and only if their
slopes are equal.
Perpendicular Lines:
Two non vertical lines are perpendicular if and only if
their slopes m_{1} and m_{2} are such that
m_{1}*m_{2} = 1
Example 1: Find the slope of a line passing
through the points
 (2 , 3) and (0 , 1)
 (2 , 4) and (2 , 6)
 (5 , 2) and (7 , 2)
Solution to Example1:
 m = (y_{2}  y_{1}) / (x_{2}  x_{1})
= (1  3) / (0  2) = 2
 m = (6  4) / (2 + 2)
The division by 2 + 2 = 0 is undefined
and the slope in this case is undefined. The line passing through the given
points is a vertical line.
 m = (2  2) / (7  5) = 0
The slope is equal to 0 and the line
through the given points is a horizontal line.
Matched Exercise 1: Find the slope of a line
passing through the points
 (2 , 7) and (2 , 1)
 (2 , 4) and (2 , 6)
 (1 , 2) and (4 , 2)
Example 2: Find the equation of the line
that passes through the point (2 , 5) and has a slope of 4.
Solution to Example 2:
 Substitute y_{1} , x_{1}
and m in the point slope form of a line
y  y_{1} = m(x  x_{1})
y  5 =  4(x  (2))
y =  4x  3
Matched Exercise 2: Find the equation of the
line that passes through the point (3 , 0) and has a slope of  1.
Example 3: Find the equation of the
line that passes through the points (0 , 1) and (3 , 5).
Solution to Example 3:
 We first calculate the slope of the line
m = (5  (1)) / (3  0) = 6 / 3 = 2
 Use the slope and any of the two points to
write the equation of the line using the point slope form.
y  y_{1} = m(x  x_{1})
using the first point
y  (1) = 2(x  0)
y = 2x  1
Matched Exercise 3: Find the equation of the
line that passes through the points (2 , 0) and (3 , 3).
Example 4: Find the slope of the line given by the equation
2x + 4y = 6
Solution to Example 4:
 Given the equation
2x + 4y = 6
 Write the equation in slope intercept form
4y = 2x + 6
y = (1/2)x + 3/2
 The slope of the line is given by the
coefficient of x and is equal to 1/2.
Matched Exercise 4: Find
the slope of the line given by the equation
x  3y = 9
Example 5: Find an equation of the line that passes through the point (2 , 3) and is parallel to the line 4x + 4y = 8
Solution to Example 5:
 Let m_{1} be the slope of the line
whose equation is to be found and m_{2} the slope of the given line. Rewrite the given equation in slope intercept form and find its slope.
4y = 4x + 8
 Divide both sides by 4
y = x + 2
slope m_{2} = 1.
 Two lines are parallel if and only if they
have equal slopes
m_{1} = m_{2} = 1
 We now use the point slope form to find
the equation of the line with slope m_{1}.
y  3 = 1(x  (2))
which may be written as
y = x + 1
Matched Exercise 5: Find an equation of the line that passes through the point (1 , 0) and is parallel to the line
2x + 2y = 8
Example 6: Find an equation of the line that passes through the point (0 , 3) and is perpendicular to the line x + y = 2.
Solution to Example 6:
 Let m_{1} be the slope of the line
whose equation is to be found and m_{2} the slope of the given line. Rewrite the given equation in slope intercept form and find its slope.
y = x + 2
slope m_{2} = 1
 Two lines are perpendicular if and only
their slopes are such that
m_{1}*m_{2} = 1
 This gives m1 = 1
 We now use the point slope form to find
the equation of the line with slope m_{1}.
y  (3) = 1(x  0)
which may be written
y = x  3
Matched Exercise 6: Find an equation of the line that passes through the point (2 , 1) and is perpendicular to the line x + 2y = 2.
More references on lines and slopes.
 Easy to use calculator to find slope and equation of a line through two points.Find Distance, Slope and Equation of Line  Calculator.
 Another calculator to find slope, x and y intercepts given the equation of a line.Find Slope and Intercepts of a Line  Calculator
 Find Distance From a Point to a Line  Calculator

Find a Parallel Line Through a Point: Find a line that is parallel to another line and passes through a point.

Find a Perpendicular Line Through a Point: Find a line that is perpendicular to another line and passes through a point.
 General Equation of a Line: ax + by = c  Applet
 Slope Intercept Form Of a Line
 Slope of a Line
