Figure 11-1: Graph of function y = 2x - 2
There are several other forms of the equation of a straight which are often useful in graphing.
Coordinate axis intercept
A straight line that intersects the x-axis at xo and the y-axis at yo is defined by the equation:
For example, a line that intercepts the x-axis at x = 1 and the y-axis at y = -2 is written as:x y --- + --- = 1 xo yo
This is another form of the linear function:x y --- - --- = 1 1 2
y = 2x - 2
Line through two points
The line through two distinct points {x1, y1} and {x2, y2} is given by:
For example, a line through the points {2, 2} and {3, 4} is written as:y - y1 y2 - y1 -------- = --------- x - x1 x2 - x1
This is also another form of the linear function:y - 2 4 - 2 ------- = ------- x - 2 3 - 2
y = 2x - 2
Point-slope
Given two points {x1, y1} and {x2, y2} on a line, its slope is defined as:
y2 - y1 rise
m = --------- = ------
x2 - x1 run
The equation of a straight line through point {a, b} with a slope of
m is:
A line is said to have positive slope if the line rises with increasing to the right; and negative slope if the line falls to the right. For example, a line through point {2, 2} with a positive slope of 2 isy = m(x - a) + b
This is again another form of the linear function:y = 2(x - 2) + 2
y = 2x - 2
Slope-intercept equation
The equation of a line with slope m and y-intercept b is
For example, a line with slope 2 and y-intercept -2 is written as the linear function:y = mx + b
This line is shown below.y = 2x - 2
Figure 11-1: Graph of function y = 2x - 2