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Chapter 1 | Functions and Graphs
this linear function can be expressed by writing
f ( x )− y 1 = m ( x − x 1 ). We call this equation the point-slope equation for that linear function.
Since every nonvertical line is the graph of a linear function, the points on a nonvertical line can be described using the slope-intercept or point-slope equations. However, a vertical line does not represent the graph of a function and cannot be expressed in either of these forms. Instead, a vertical line is described by the equation x = k for some constant k . Since neither the slope-intercept form nor the point-slope form allows for vertical lines, we use the notation ax + by = c , where a , b are both not zero, to denote the standard form of a line .
Definition Consider a line passing through the point ( x 1 , y 1 ) with slope m . The equation
y − y 1 = m ( x − x 1 )
(1.4)
is the point-slope equation for that line. Consider a line with slope m and y -intercept (0, b ). The equation
y = mx + b
(1.5)
is an equation for that line in slope-intercept form . The standard form of a line is given by the equation
ax + by = c , where a and b are both not zero. This form is more general because it allows for a vertical line, x = k .
(1.6)
Example 1.12 Finding the Slope and Equations of Lines
Consider the line passing through the points (11, −4) and (−4, 5), as shown in Figure 1.17 .
This OpenStax book is available for free at http://cnx.org/content/col11964/1.12
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