Unformatted text preview: rcept of the line y = mx + b is (0, b).
Equation 2.3. The slope-intercept form of the line with slope m and y -intercept (0, b) is the
equation y = mx + b.
Note that if we have slope m = 0, we get the equation y = b which matches our formula for a
horizontal line given in Section 1.2. The formula given in Equation 2.3 can be used to describe all
lines except vertical lines. All lines except vertical lines are functions (why?) and so we have ﬁnally
reached a good point to introduce linear functions.
3 We can also understand this equation in terms of applying transformations to the function I (x) = x. See the
exercises. 116 Linear and Quadratic Functions Definition 2.1. A linear function is a function of the form
f (x) = mx + b,
where m and b are real numbers with m = 0. The domain of a linear function is (−∞, ∞).
For the case m = 0, we get f (x) = b. These are given their own classiﬁcation.
Definition 2.2. A constant function is a function of the form
f (x) = b,
where b is real number....
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