This preview shows page 1. Sign up to view the full content.
Unformatted text preview: re incorrect. Rather, it means that the temperature change
throughout the day isn’t a constant 2◦ F per hour. Mathematics is often used to describe, or model,
real world phenomena. Mathematical models are just that: models. The predictions we get out
of the models may be mathematically accurate, but may not resemble what happens in the real
world. We will discuss this more thoroughly in Section 2.5.
In Section 1.2, we discussed the equations of vertical and horizontal lines. Using the concept of
slope, we can develop equations for the other varieties of lines. Suppose a line has a slope of m and
contains the point (x0 , y0 ). Suppose (x, y ) is another point on the line, as indicated below.
(x, y )
(x0 , y0 ) 2.1 Linear Functions 115 We have
y − y0
x − x0
m ( x − x 0 ) = y − y0
y − y0 = m (x − x0 )
y = m (x − x0 ) + y0 .
m= We have just derived the point-slope form of a line.3
Equation 2.2. The point-slope form of the line with slope m containing the point (x0 , y0 ) is
the equation y = m (x − x0 ) + y0 .
Example 2.1.3. Write the equation of the line cont...
View Full Document