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.

Match Linear Equations to Graphs. Excellent interactive activity where linear equations are matched to graphs.

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
