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