1.5 linear equations mr. anderson pre calculus falconer central school 2010
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1.5Linear Equations
Mr. AndersonPre Calculus
Falconer Central School2010
Linear Equations
A linear equation is a polynomial equation in which the degree is one.
The degree of an equation is the highest power on the independent variable.
A linear equation will look like a line when graphed (hence the name “linear equation”).
A Couple Forms
Explicit – Solved for the dependent variable
Implicit – Solved for the constant
*Note that polynomial equations are typically written in explicit forms.
y =3x+ 2
y−3x=2
Slope – Intercept Form
This is the form that we are used to. It requires a slope, and a y-intercept (hence the name).
y =mx+b
Point-Slope Form
This form is useful when you know a point and a slope (hence the name).
y−y1 =m x−x1( )
Example 1
Write the equation of the line passing through the point (2, 3) and having a slope of -2.
y−y1 =m x−x1( )
y−3 =−2 x−2( )
y−3 =−2x+ 4
y =−2x+ 7
or
y =mx+b
3=−2 2( ) +b
7 =b
∴ y = −2x + 7
Example 2
Write the equation of the line passing through the points (0, -4) and (2, 10).
Example 3
Suppose that in the Creative Design model of the Universe, the designer got lazy and decided that the height to weight ratio of all animals should be linear. That is, a dog that measures 1 – foot in height would weigh 14 pounds, and an elephant that is 11 feet tall would weigh 8000 pounds. In this linear model, how much would a 6 foot tall person weigh?
Practice
Pg. 40 # 15-20 [3], 21-26 [3], 35