Linear Expressions Chapter 3
What do you know about Linear Relations?
What does Linear look like? 0 On a graph- 0 In a table – 0 As an equation- 0 Straight line 0 Constant rate of change 0 Unit rate is always the same 0 Ratio of Change in y divided by the change in x The x and y variables have an exponent of 1
Which are Linear Equations Y = 4 – 3x 2x – 3y = 5 2/3x – 1/4y = 12 X 2 – 3 = y 8 = x/y 1/3 y = -1 6x – 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 Equations y = 4 – 3x 2/3x – 1/4y = 5 1/3 y = -1 -5x + 2y = -9 4/5y – 2/3x = 3/2 Standard Form 3x + y = 4 8x – 3y = 60 y = -3 5x – 2y = 9 20x – 24y = 45
Intercepts 0 X- Intercept 0 Where the line passes through the x axis 0 Set y=0 0 In a table, where y = 0 0 Y- Intercept 0 Where the line passes through the x axis 0 Set x = 0 0 In a table, where x = 0
Graphing Equations in Standard Form 0 Using an Equation in Standard Form 0 Two Points determine a line 0 Find the X and Y intercepts 2x + 4y = 16 y = 4 – 3x 1/3y = -1 x = 2/5y + 4
Graphing Relations in a Table 0 Using a Table of Values 0 Find three to four points in a T-chart and plot the points Y = 1/3x + 5 2x – y = 2 X = 3
Which equations are Linear?? 2x – 8 = y 6 = 2/5 x – y 2x 2 – y = 8 xy = x -6 = 3x + 1 2x – 4 = 2x - 6
Linear Equations have one or no solutions 0 The solution or root of a function is any value that makes the equation true 0 The value that makes the equation true is the x-intercept
Function Notation and Roots of an Equation 0 A linear function is a function for which the graph is a line 0 The simplest linear function is f(x) = x 0 You 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 – y 3x + 7 = 3x + 1 2x – 8 = 2(x – 4) 0 Steps f(x) = 0 0 = 2x – 8 0 = 2/5 x – 6 No solution, no x-intercept horizontal line Infinite solutions 0 Non-linear