Linear Expressions

Chapter 3

What do you know about Linear Relations?

What does Linear look like?

0On a graph-

0 In a table –

0As an equation-

0Straight line

0Constant rate of change0 Unit rate is always the

same0 Ratio of Change in y

divided by the change in x

The x and y variables have an exponent of 1

Which are Linear EquationsY = 4 – 3x2x – 3y = 52/3x – 1/4y = 12X2 – 3 = y8 = x/y1/3 y = -16x – xy = 8

Standard Form

The standard Form of a Linear Equation is Ax + By = C, where A > 0, and A, B, and C are all integers with a GCF of 1.

Put Each in Standard Form

Linear Equationsy = 4 – 3x2/3x – 1/4y = 51/3 y = -1-5x + 2y = -94/5y – 2/3x = 3/2

Standard Form3x + y = 48x – 3y = 60y = -35x – 2y = 920x – 24y = 45

Intercepts

0X- Intercept0Where the line

passes through the x axis0Set y=00In a table, where

y = 0

0Y- Intercept0Where the line

passes through the x axis0Set x = 00In a table, where

x = 0

Graphing Equations in Standard Form

0Using an Equation in Standard Form0Two Points

determine a line0Find the X and Y

intercepts

2x + 4y = 16y = 4 – 3x1/3y = -1x = 2/5y + 4

Graphing Relations in a Table

0Using a Table of Values0 Find three to

four points in a T-chart and plot the points

Y = 1/3x + 52x – y = 2X = 3

Which equations are Linear??

2x – 8 = y6 = 2/5 x – y2x2 – y = 8xy = 67 + 3x -6 = 3x + 12x – 4 = 2x - 6

Linear Equations have one or no solutions

0The solution or root of a function is any value that makes the equation true0The value that makes the equation

true is the x-intercept

Function Notation and Roots of an Equation

0A linear function is a function for which the graph is a line0The simplest linear function is f(x) = x0You can find the root of an equation by

graphing it’s related function. To write the related function replace y with f(x) and set f(x)=0.

Find the Zeros, Roots, Solutions

2x – 8 = y

6 = 2/5 x – y3x + 7 = 3x + 12x – 8 = 2(x – 4)

0Stepsf(x) = 0

0 = 2x – 80 = 2/5 x – 6No solution, no x-intercept

horizontal lineInfinite solutions

0 Non-linear